[And] R. J., Anderson, On the function Z(t) associated with the Riemann zetafunction, J. Math. Anal. Appl. 118 (1986), 323–340.Google Scholar

[AGZ] G. W., Anderson, A., Guionnet and O., Zeitouni, An Introduction to Random Matrices, Cambridge University Press, Cambridge, 2010.

[Ape] R., Apéry, Interpolation de fractions continues et irrationalité de certaines constantes, Math. CTHS Bull. Sec. Sci. II (Bibl. Nat. Paris), 1981, 37–53.

[Atk1] F. V., Atkinson, The mean value of the zeta-function on the critical line, Quart. J. Math. Oxford 10 (1939), 122–128.Google Scholar

[Atk2] F. V., Atkinson, The mean value of the zeta-function on the critical line, Proc. London Math. Soc. 47 (1941), 174–200.Google Scholar

[Atk3] F. V., Atkinson, A mean value property of the Riemann zeta-function, J. London Math. Soc. 23 (1948), 128–135.Google Scholar

[Atk4] F. V., Atkinson, The mean value of the Riemann zeta-function, Acta Math. 81 (1949), 353–376.Google Scholar

[Bac] R. J., Backlund, Sur les zéros de la fonction ζ(s) de Riemann, Comptes Rendus Acad. Sci. 158 (1914), 1979–1982.Google Scholar

[Bet] S., Bettin, The second moment of the Riemann zeta-function with unbounded shifts, preprint available at arXiv:1111.0925.

[Boc] S., Bochner, On Riemann's functional equation with multiple gamma factors, Annals of Math. 67 (1958), 29–41.Google Scholar

[BoHe] E., Bombieri and D., Hejhal, Sur les zéros des fonctions zeta d'Epstein, Comptes Rendus Acad. Sci. Paris 304 (1987), 213–217.Google Scholar

[BoIw1] E., Bombieri and H., Iwaniec, On the order of ζ(½ + it), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)13 (1986), 449–472.Google Scholar

[BoIw2] E., Bombieri and H., Iwaniec, Some mean value theorems for exponential sums, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), 473–486.Google Scholar

[BoGh] E., Bombieri and A., Ghosh, Around the Davenport-Heilbronn function, Russian Math. Surveys 66 (2011), 221–270,

Uspekhi Mat. Nauk 66 (2011), 15–66.

[Bom1] E., Bombieri, Riemann Hypothesis. The Millennium Prize Problems, Clay Math. Inst., Cambridge, MA, 2006, pp. 107–124.

[Bom2] E., Bombieri, The classical theory of zeta and L-functions, Milan J.Math. 78 (2010), 11–59.Google Scholar

[BCRW] P., Borwein, S., Choi, B., Rooney and A., Weirathmueller, The Riemann Hypothesis, a Resource for the Afficionado and the Virtuoso Alike, CMS Books in Mathematics, Canadian Math. Soc., 2008.

[BCY] H., Bui, B., Conrey and M. P., Young, More than 41% of the zeros of the zeta function are on the critical line, to appear in Acta Arith., see arXiv:1002.4127.

[BhS1] G., Bhowmik and J.-C., Schlage-Puchta, Natural boundaries of Dirichlet series, Func. Approx. Comment. Math. 37 (2007), 17–29.Google Scholar

[BhS2] G., Bhowmik and J.-C., Schlage-Puchta, Essential singularities of Euler products, to appear, preprint available at arXiv:1001.1891.

[Bre] J., Bredberg, Large gaps between consecutive zeros on the critical line of the Riemann zeta-function, to appear, preprint available at arXiv:1101.3197.

[Bui] H. M., Bui, Large gaps between consecutive zeros of the Riemann zeta-function, J. Number Theory 131 (2011), 67–95.Google Scholar

[Cha] K., Chandrasekharan, Arithmetical Functions, Springer Verlag, Berlin-Heidelberg-New York, 1970.

[ChNa] K., Chandrasekharan and R., Narasimhan, Functional equations with multiple gamma factors and the average order of arithmetic functions, Annals of Math. 76 (1962), 93–136.Google Scholar

[ChSo] V., Chandee and K., Soundararajan, Bounding ∣ζ(½ + it)∣ on the Riemann Hypothesis, Bull. London Math. Soc. (2011), 243–250.

[CMoP] E., Carletti, G. Monti, Bragadin and A., Perelli, On general L-functions, Acta Arith. 66 (1994), 147–179.Google Scholar

[Con1] J. B., Conrey, The fourth moment of derivatives of the Riemann zeta-function, Quarterly J. Math., Oxf. II. Ser. 39 (1988), No. 153, 21–36.Google Scholar

[Con2] J. B., Conrey, More than two fifths of the zeros of the Riemann zeta function are on the critical line, J. Reine Angew. Math. 399 (1989), 1–26.Google Scholar

[Con3] J. B., Conrey, A note on the fourth power moment of the Riemann zeta-function, in: B. C., Berndt et al.(eds.) Analytic Number Theory. Vol. 1. Proc. of a Conf. in Honor of Heini Halberstam, Urbana, 1995, Birkhäuser, Prog. Math. 138 (1996), 225–230.

[Con4] J. B., Conrey, The Riemann hypothesis, Notices Amer. Math. Soc. 50 (2003), 341–353.Google Scholar

[CoGh1] J. B., Conrey and A., Ghosh, A mean value theorem for the Riemann zeta-function at its relative extrema on the critical line, J. Lond. Math. Soc., II. Ser. 32 (1985), 193–202.Google Scholar

[CoGh2] J. B., Conrey and A., Ghosh, A simpler proof of Levinson's theorem, Math. Proc. Camb. Phil. Soc. 97 (1985), 385–395.Google Scholar

[CoGh3] J. B., Conrey and A., Ghosh, On the Selberg class of Dirichlet series: small degrees, Duke Math. J. 72 (1993), 673–693.Google Scholar

[CGG1] J. B., Conrey, A., Ghosh and S. M., Gonek, A note on gaps between zeros of the zeta-function, Bull. London Math. Soc. 16 (1984), 421–424.Google Scholar

[CGG2] J. B., Conrey, A., Ghosh and S. M., Gonek, Large gaps between zeros of the zeta-function, Mathematika 33 (1986), 212–238.Google Scholar

[CGG3] J. B., Conrey, A., Ghosh and S. M., Gonek, Simple zeros of the Riemann zeta-function, Proc. Lond. Math. Soc., III. Ser. 76 (1998), No. 3, 497–522.Google Scholar

[CFKRS1] J. B., Conrey, D. W., Farmer, J. P., Keating, M. O., Rubinstein and N. C., Snaith, Integral moments of L-functions, Proc. London Math. Soc. (3) 91 (2005), 33–104.Google Scholar

[CFKRS2] J. B., Conrey, D. W., Farmer, J. P., Keating, M. O., Rubinstein and N. C., Snaith, Lower order terms in the full moment conjecture for the Riemann zeta function, J. Number Theory 128 (2008), 1516–1554.Google Scholar

[CoGo] J. B., Conrey and S. M., Gonek, High moments of the Riemann zeta-function, Duke Math. J. 107 (2001), 577–604.Google Scholar

[COSV] G., Csordas, A. M., Odlyzko, W., Smith and R. S., Varga, A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant LAMBDA, Electr. Trans. Num. Anal. 1 (1993), 104–111.Google Scholar

[Dah] G., Dahlquist, On the analytic continuation of Eulerian products, Ark. Mat. 1 (1952), 533–554.Google Scholar

[DaHe] H., Davenport and H., Heilbronn, On the zeros of certain Dirichlet series I, II, J. London Math. Soc. 11 (1936), 181–185Google Scholar

H., Davenport and H., Heilbronn, On the zeros of certain Dirichlet series I, II, J. London Math. Soc. 11 (1936), 307–312.Google Scholar

[Del] H., Delange, Généralisation du théorème de Ikehara, Annales scien. E.N.S. 71 (1954), 213–242.Google Scholar

[Deli] P., Deligne, La conjecture de Weil. I., Publications Mathématiques de l'IHÉS 43 (1974), 273–307.Google Scholar

[DGG] A., Diaconu, P., Garrett and D., Goldfeld, Natural boundaries and a correct notion of integral moments of L-functions, preprint, 2009.

[DGH] A., Diaconu, D., Goldfeld and J., Hoffstein, Multiple Dirichlet series and moments of zeta and L-functions, Compositio Math. 139, No. 3 (2003), 297–360.Google Scholar

[Edw] H. M., Edwards, Riemann's Zeta-Function, Academic Press, New York- London, 1974 (Dover Publications Inc., Mineola, NY, 2001. Reprint of the 1974 original).

[EMOT] A., Erdélyi, W., Magnus, F., Oberhettinger and F. G., Tricomi, Higher Transcendental Functions, Volume I, McGraw-Hill, 1953.

[Est1] T., Estermann, On certain functions represented by Dirichlet series, Proc. London Math. Soc. 27 (1928), 435–448.Google Scholar

[Est2] T., Estermann, Introduction to Modern Prime Number Theory, Cambridge University Press, Cambridge, 1969.

[Eul] L., Euler, Remarques sur un beau rapport entre les séries des puissances tout directes que réciproques, Mém. Acad. Roy. Sci. Belles Lettres 17 (1768), 83–106.Google Scholar

[Fen] S., Feng, Zeros of the Riemann zeta-function on the critical line, to appear, preprint available at arXiv:1003.0059.

[FGH] D. W., Farmer, S. M., Gonek and C. P., Hughes, The maximum size of L-functions. J. Reine Angew. Math. 609 (2007), 215–236.Google Scholar

[Fla] C., Flammer, Spheroidal Wave Functions, Stanford University Press, Stanford, CA, 1957.

[For1] K., Ford, Vinogradov's integral and bounds for the Riemann zeta-function, Proc. London Math. Soc. III Ser. 85 (2002), 565–633.Google Scholar

[For2] K., Ford, Zero-free regions for the Riemann zeta-function, in: M. A., Bennett et al. (ed.) Number Theory for the Millennium II. Proc. of the Conf. on number theory, Urbana-Champaign, IL, USA, 2000. Natick, MA: A. K. Peters, 25–56 (2002).

[Fuj1] A., Fujii, On the distribution of zeros of the Riemann zeta function in short intervals, Bull. Amer. Math. Soc. 81 (1975), 139–142.Google Scholar

[Fuj2] A., Fujii, On the difference between r consecutive ordinates of the zeros of the Riemann zeta function, Proc. Japan Acad. 51 (1975), 741–743.Google Scholar

[Gab] W., Gabcke, Neue Herleitung und explizite Restabschätzung der Riemann-Siegel Formel, Univ. Göttingen, Ph.D. Dissertation, Göttingen, 1979, pp. 153.

[Gho] A., Ghosh, On the Riemann zeta function-mean value theorems and the distribution of |S(T)|, J. Number Theory 17 (1983), 93–102.Google Scholar

[Gol1] D. A., Goldston, Large differences between consecutive prime numbers, Ph.D. thesis, University of California, Berkeley, 1981.

[Gol2] D. A., Goldston, On the pair correlation conjecture for zeros of the Riemann zeta-function, J. Reine Angew. Math. 385 (1988), 24–40.Google Scholar

[Gol3] D. A., Goldston, Notes on pair correlation of zeros and prime numbers, in: F., Mezzadri et al.(eds.) Recent Perspectives in Random Matrix Theory and Number Theory, Proc. “Random Matrix Approaches in Number Theory”, London Mathematical Society Lecture Note Series, 322, Cambridge University Press, Cambridge (2005), 79–110.

[GoGo] D. A., Goldston and S. M., Gonek, A note on S(t) and the zeros of the Riemann zeta-function, Bull. London Math. Soc. 39 (2007), 482–486.Google Scholar

[GoMo] D. A., Goldston and H. L, Montgomery, Pair Correlation and Primes in Short Intervals, Analytic Number Theory and Diophantine Problems, Birkhäuser, Boston, Mass., 1987, pp. 187–203.

[Gon] S. M., Gonek, On negative moments of the Riemann zeta-function, Mathematika 36 (1989), 71–88.Google Scholar

[GrKo] S. W., Graham and G., Kolesnik, Van der Corput's method for exponential sums, London Mathematical Society Lecture Note Series, 126, Cambridge University Press, Cambridge, 1991.

[Gourd] X., Gourdon, The first 1013 zeros of the Riemann zeta-function and zeros computation at very large height, 2004, http://numbers.computation.free.fr/Constants/Miscellaneous.

[Gours]É., Goursat, Cours d'Analyse Mathématique, Dover, New York, 1959.

[Gra] J. P., Gram, Sur les zéros de la fonction de Riemann, Acta Mathematica 27 (1903), 289–304.Google Scholar

[Hal1] R. R., Hall, The behaviour of the Riemann zeta-function on the critical line, Mathematica 46 (1999), 281–313.Google Scholar

[Hal2] R. R., Hall, A Wirtinger type inequality and the spacing between the zeros of the Riemann zeta-function, J. Number Theory 93 (2002), 235–245.Google Scholar

[Hal3] R. R., Hall, On the extreme values of the Riemann zeta-function between its zeros on the critical line, J. Reine Angew. Math. 560 (2003), 29–41.Google Scholar

[Hal4] R. R., Hall, Generalized Wirtinger inequalities, random matrix theory, and the zeros of the Riemann zeta-function, J. Number Theory 97 (2002), 397–409.Google Scholar

[Hal5] R. R., Hall, On the stationary points of Hardy's function Z(t), Acta Arith. 111 (2004), 125–140.Google Scholar

[Hal6] R. R., Hall, A new unconditional result about large spaces between zeta zeros, Mathematika 53 (2005), 101–113.Google Scholar

[Hal7] R. R., Hall, Extreme values of the Riemann zeta-function on short zero intervals, Acta Arith. 121 (2006), 259–273.Google Scholar

[Ham] H., Hamburger, Über die Riemmansche Funkionalgleichung der ζ- Funktion I, II, III, Math. Zeit. 10 (1921), 240–254Google Scholar

H., Hamburger, Über die Riemmansche Funkionalgleichung der ζ- Funktion I, II, III, Math. Zeit. (1922), 224–245Google Scholar

H., Hamburger, Über die Riemmansche Funkionalgleichung der ζ- Funktion I, II, III, Math. Zeit. 13 (1922), 283–311.Google Scholar

[HaIv1] J. L., Hafner and A., Ivić, On some mean value results for the Riemann zeta-function, Proceedings International Number Theory Conference Québec 1987, Walter de Gruyter and Co., 1989, Berlin-New York, pp. 348–358.

[HaIv2] J. L., Hafner and A., Ivić, On the mean square of the Riemann zeta-function on the critical line, J. Number Theory 32 (1989), 151–191.Google Scholar

[Har] G., Harcos, Uniform approximate functional equation for principal L-functions, Inter. Math. Research Notices 18 (2002), 923–932.Google Scholar

[Har1] G. H., Hardy, On the zeros of Riemann's zeta-function, Proc. London Math. Soc. Ser. 2 13 (records of proceedings at meetings), March 1914.Google Scholar

[Har2] G. H., Hardy, Sur les zéros de la fonction ζ(s) de Riemann, Comptes Rendus Acad. Sci. (Paris) 158 (1914), 1012–1014.Google Scholar

[Har3] G. H., Hardy, A Mathematician's Apology, Cambridge University Press, Cambridge (1940), 2004 reissue.

[Har4] G. H., Hardy, Ramanujan, Cambridge University Press, London, 1940, reissue AMS Chelsea Pub., 1999.

[Har5] G. H., Hardy, Divergent Series, Clarendon Press, Oxford, 1949.

[Har6] G. H., Hardy, A Course of Pure Mathematics (10th edn). Cambridge University Press, Cambridge (1952) [1908], 2008 reissue.

[Har7] G. H., Hardy, Collected Papers of G. H. Hardy; Including Joint papers with J.E. Littlewood and Others, London Mathematical Society, 1966.

[HaLi1] G. H., Hardy and J. E., Littlewood, Contributions to the theory of the Riemann zeta-function and the distribution of primes, Acta Math. 41 (1918), 119–196.Google Scholar

[HaLi2] G. H., Hardy and J. E., Littlewood, The zeros of Riemann's zeta-function on the critical line, Math. Zeitschrift 10 (1921), no. 3–4, 283–317.Google Scholar

[HaLi3] G. H., Hardy and J. E., Littlewood, The approximate functional equation for ζ(s)and ζ2(s), Proc. London Math. Soc.(2) 29 (1929), 81–97.Google Scholar

[HaRi] G. H., Hardy and M., Riesz, The General Theory of Dirichlet Series, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1915.

[Has] C. B., Haselgrove, Tables of the Riemann Zeta Function, Cambridge University Press, Cambridge, 1960.

[HaWr] G. H., Hardy and E. M., Wright, An Introduction to the Theory of Numbers (6th edn), Oxford University Press, Oxford, 2008.

[Hea1] D. R., Heath-Brown, The twelfth power moment of the Riemann zeta-function, Quart. J. Math.(Oxford) 29 (1978), 443–462.Google Scholar

[Hea2] D. R., Heath-Brown, The mean value theorem for the Riemann zeta-function, Mathematika 25 (1978), 177–184.Google Scholar

[Hea3] D. R., Heath-Brown, The fourth power moment of the Riemann zeta function, J. London Math. Soc. (3)38 (1979), 385–422.Google Scholar

[Hea4] D. R., Heath-Brown, Fractional moments of the Riemann zeta-function, J. London Math. Soc. 24 (1981), 65–78.Google Scholar

[Hej1] D. A., Hejhal, On the distribution of ∣log ζ′ (½ + it)∣, in: K. E., Aubert et al. (eds.) Number Theory, Trace Formulas and Discrete Groups, Proceedings Selberg 1987 Symposium, Academic Press, 1989, 343–370.

[Hej2] D. A., Hejhal, On a result of Selberg concerning zeros of linear combinations of L-functions, Int. Math. Res. Not. 11 (2000), 551–577.Google Scholar

[HiOd1] G. A., Hiary and A. M., Odlyzko, The zeta function on the critical line: numerical evidence for moments and random matrix theory models, to appear, preprint available at arXiv:1008.2173.

[HiOd2] G. A., Hiary and A. M., Odlyzko, Numerical study of the derivative of the Riemann zeta-function at zeros, to appear, preprint available at arXiv:1105.4312.

[HKN] C. P., Hughes, J. P., Keating and O., Neil, Random matrix theory and the derivative of the Riemann zeta function, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456 (2000), 2611–2627.Google Scholar

[Hut] J. I., Hutchinson, On the roots of the Riemann zeta-function, V. Trans. Amer. Math. Soc. 27 (1925), 27–49.Google Scholar

[Hux1] M. N., Huxley, Area, Lattice Points and Exponential Sums, Oxford Science Publications, Clarendon Press, Oxford, 1996.

[Hux2] M. N., Huxley, Exponential sums and the Riemann zeta function V, Proc. London Math. Soc.(3) 90 (2005), 1–41.Google Scholar

[HuIv] M. N., Huxley and A., Ivić, Subconvexity for the Riemann zeta-function and the divisor problem, Bulletin CXXXIV de l'Académie Serbe des Sciences et des Arts - 2007, Classe des Sciences Mathématiques et Naturelles, Sciences Mathématiques 32, 13–32.

[Ing] A. E., Ingham, Mean-value theorems in the theory of the Riemann zeta-function, Proc. London Math. Soc.(2) 27 (1926), 273–300.Google Scholar

[Isr1] M. I., Israilov, Coefficients of the Laurent expansion of the Riemann zeta-function (Russian), Dokl. Akad. Nauk SSSR 12 (1979), 9–10.Google Scholar

[Isr2] M. I., Israilov, The Laurent expansion of the Riemann zeta-function (Russian), Trudy Mat. Inst. Steklova 158 (1981), 98–104.Google Scholar

[Iv1] A., Ivić, The Riemann Zeta-Function, John Wiley & Sons, New York, 1985 (reissue, Dover, Mineola, New York, 2003).

[Iv2] A., Ivić, On consecutive zeros of the Riemann zeta-function on the critical line, in: Séminaire de Théorie des Nombres, Université de Bordeaux 1986/87, Exposé no. 29, 14 pp.

[Iv3] A., Ivić, On a problem connected with zeros of ζ(s) on the critical line, Monatshefte Math. 104 (1987), 17–27.Google Scholar

[Iv4] A., Ivić, Mean Values of the Riemann Zeta-function, LN's 82, Tata Inst. of Fundamental Research, Bombay, 1991 (Springer Verlag, Berlin).

[Iv5] A., Ivić, On the fourth moment of the Riemann zeta-function, Publs. Inst. Math. (Belgrade) 57(71) (1995), 101–110.Google Scholar

[Iv6] A., Ivić, On sums of gaps between the zeros of ζ(s) on the critical line, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 6 (1995), 55–62.Google Scholar

[Iv7] A., Ivić, An approximate functional equation for a class of Dirichlet series, Journal of Analysis 3 (1995), 241–252.Google Scholar

[Iv8] A., Ivić, The Mellin transform and the Riemann zeta-function, in: W. G., Nowak and J. Schoißengeier, Vienna (eds.) Proceedings of the Conference on Elementary and Analytic Number Theory (Vienna, July 18–20, 1996), Universität Wien & Universität für Bodenkultur, 1996, 112–127.

[Iv9] A., Ivić, On the error term for the fourth moment of the Riemann zeta-function, J. London Math. Soc. 60 (2)(1999), 21–32.Google Scholar

[Iv10] A., Ivić, The Laplace transform of the fourth moment of the zeta-function, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11 (2000), 41–48.Google Scholar

[Iv11] A., Ivić, On some conjectures and results for the Riemann zeta-function, Acta. Arith. 99 (2001), 115–145.Google Scholar

[Iv12] A., Ivić, The Laplace transform of the fourth moment of of the zeta-function, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11 (2000), 41–48.Google Scholar

[Iv13] A., Ivić, On small values of the Riemann zeta-function on the critical line and gaps between zeros, Lietuvos Mat. Rinkinys 42 (2002), 31–45.Google Scholar

[Iv14] A., Ivić, On the estimation of Ƶ2(s), in: Anal. Probab. Methods Number Theory, A., Dubickas et al. (eds.) TEV, Vilnius, 2002, 83–98.

[Iv15] A., Ivić, On the integral of Hardy's function, Arch. Mathematik 83 (2004), 41–47.Google Scholar

[Iv16] A., Ivić, The Mellin transform of the square of Riemann's zeta-function, International J. of Number Theory 1 (2005), 65–73.Google Scholar

[Iv17] A., Ivić, On the estimation of some Mellin transforms connected with the fourth moment of ∣ζ(½ + it)∣, in: W., Schwarz and J., Steuding (eds.) Elementare und Analytische Zahlentheorie (Tagungsband), Proceedings ELAZ-Conference May 24–28, 2004, Franz Steiner Verlag, 2006, 77–88.

[Iv18] A., Ivić, On some reasons for doubting the Riemann Hypothesis, in: P., Borwein et al.(eds.) The Riemann Hypothesis, CMS Books in Mathematics, Springer, 2008.

[Iv19] A., Ivić, On the moments of the Riemann zeta-function in short intervals, Hardy-Ramanujan Journal 32 (2009), 4–23.Google Scholar

[Iv20] A., Ivić, On the Mellin transforms of powers of Hardy's function, Hardy- Ramanujan Journal 33 (2010), 32–58.Google Scholar

[Iv21] A., Ivić, On some problems involving Hardy's function, Central European J. Math. 8(6) (2010), 1029–1040.Google Scholar

[IvJu] A., Ivić and M., Jutila, Gaps between consecutive zeros of the Riemann zeta-function, Monatshefte Math. 105 (1988), 59–73.Google Scholar

[IJM] A., Ivić, M., Jutila and Y., Motohashi, The Mellin transform of powers of the Riemann zeta-function, Acta Arith. 95 (2000), 305–342.Google Scholar

[IvMo1] A., Ivić and Y., Motohashi, A note on the mean value of the zeta and L-functions VII, Proc. Japan Acad. Ser. A 66 (1990), 150–152.Google Scholar

[IvMo2] A., Ivić and Y., Motohashi, The mean square of the error term for the fourth moment of the zeta-function, Proc. London Math. Soc. (3)66 (1994), 309–329.Google Scholar

[IvMo3] A., Ivić and Y., Motohashi, The fourth moment of the Riemann zeta-function, J. Number Theory 51 (1995), 16–45.Google Scholar

[IvPe] A., Ivić and A., Perelli, Mean values of certain zeta-functions on the critical line, Litovskij Mat. Sbornik 29 (1989), 701–714.Google Scholar

[Iwa1] H., Iwaniec, Introduction to the Spectral Theory of Automorphic Forms, Bibl. de la Revista Iberoamericana, Madrid, 1995.

[Iwa2] H., Iwaniec, Topics in Classical Automorphic Forms, Graduate Studies in Mathematics 17, American Mathematical Society, Providence, RI, 1997.

[Iwa3] H., Iwaniec, Spectral Methods of Automorphic Forms, 2nd edn, Graduate Studies in Mathematics, 53, American Mathematical Society, Providence, RI, 1997.

[Joy] D., Joyner, Distribution Theorems of L-functions, Pitman Research Notes in Mathematics Series 142, Longman Scientific & Technical, Harlow, John Wiley & Sons, New York, 1986.

[Jut1] M., Jutila, On the value distribution of the zeta-function on the critical line, Bull. London Math. Soc. 15 (1983), 513–518.Google Scholar

[Jut2] M., Jutila, Mean values of Dirichlet series via Laplace transforms, in: Y., Motohashi (ed.) Analytic Number Theory, London Math. Soc. LNS 247, Cambridge University Press, Cambridge, 1997, 169–207.

[Jut3] M., Jutila, Atkinson's formula revisited, in: Voronoï's Impact on Modern Science, Book 1, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 1998, 137–154.

[Jut4] M., Jutila, The Mellin transform of the square of Riemann's zeta-function, Periodica Math. Hung. 42 (2001), 179–190.Google Scholar

[Jut5] M., Jutila, The Mellin transform of the fourth power of the Riemann zeta-function, in: S. D, Adhikari, et al.(eds.) Number Theory. Proc. Inter. Conf. on Analytic Number Theory with special emphasis on L-functions, held at the Inst. Math. Sc., Chennai, India, January 2002. Ramanujan Math. Soc. LNS 1 (2005), 15–29.

[Jut6] M., Jutila, Atkinson's formula for Hardy's function, J. Number Theory 129 (2009), 2853–2878.Google Scholar

[Jut7] M., Jutila, An estimate for the Mellin transform of Hardy's function, Hardy- Ramanujan J. 33 (2010), 23–31.Google Scholar

[Jut8] M., Jutila, The Mellin transform of Hardy's function is entire (in Russian), Mat. Zametki 88 (4) (2010), 635–639.Google Scholar

[Jut9] M., Jutila, An asymptotic formula for the primitive of Hardy's function, Arkiv Mat. 49, No. 1, (2011), 97–107.Google Scholar

[Kac] J., Kaczorowski, Axiomatic theory of L-functions: the Selberg class, in: A., Perelli and C., Viola (eds.) Analytic Number Theory, Springer Verlag, Berlin-Heidelberg, 2006, 133–209.

[KaKo] A. A., Karatsuba and M. A., Korolev, The argument of the Riemann zeta function (English translation of Russian original)Russ. Math. Surv. 60 (2005), No. 3, 433–488;Google Scholar

translation from Usp. Mat. Nauk 60 (2005), No. 3, 41–96.

[KaPe1] J., Kaczorowski and A., Perelli, The Selberg class: a survey, in: Number Theory in Progress, Vol. 2 (Zakopane-Koscielisko, 1997), de Gruyter, Berlin, 1999, 953–992.

[KaPe2] J., Kaczorowski and A., Perelli, On the structure of the Selberg class, I: 0 ≤ d ≤ 1, Acta Math. 182 (1999), 207–241.Google Scholar

[KaPe3] J., Kaczorowski and A., Perelli, On the structure of the Selberg class, V: 1 < d < 5/3, Invent. Math. 150 (2002), 485–516.Google Scholar

[KaPe4] J., Kaczorowski and A., Perelli, On the structure of the Selberg class, VI: non-linear twists, Acta Arith. 116 (2005), 315–341.Google Scholar

[KaPe5] J., Kaczorowski and A., Perelli, On the structure of the Selberg class, VII: 1 < d < 2, Annals of Math. 173 (2011), 1397–1441.Google Scholar

[Kar1] A. A., Karatsuba, On the distance between adjacent zeros of the Riemann zeta-function lying on the critical line (Russian), Trudy Mat. Inst. Steklova 157 (1981), 49–63.Google Scholar

[Kar2] A. A., Karatsuba, On the zeros of the Davenport-Heilbronn function lying on the critical line (Russian), Izv. Akad. Nauk SSSR ser. mat. 54 no. 2 (1990), 303–315.Google Scholar

[KaS] J., Kalpokas and J., Steuding, On the value-distribution of the Riemann zeta-function on the critical line, Moscow Journal of Combinatorics and Number Theory 1 (2011), 26–42.Google Scholar

[KaVo] A. A., Karatsuba and S. M., Voronin, The Riemann Zeta-Function, Walter de Gruyter, Berlin-New York, 1992.

[Kea] J., Keating, The Riemann zeta-function and quantum chaology, Proc. Internat. School of Phys. Enrico Fermi CXIX (1993), 145–185.Google Scholar

[KeSn] J. P., Keating and N.C., Snaith, Random matrix theory and L-functions at s = 1/2, Comm. Math. Phys. 214 (2000), 57–89.Google Scholar

[Kob] H., Kober, Eine Mittelwertformel der Riemannschen Zetafunktion, Compositio Math. 3 (1936), 174–189.Google Scholar

[Kol] G., Kolesnik, On the estimation of multiple exponential sums, in: Recent Progress in Analytic Number Theory, Symp. Durham 1979 (Vol. 1), Academic Press, London, 1981, 231–246.

[Kore] J., Korevaar, Tauberian Theory, Grund. der math. Wissenschaften Vol. 329, Springer, Berlin, 2004.

[Kor1] M. A., Korolev, On the argument of the Riemann zeta function on the critical line. (English translation of Russian original)Izv. Math. 67 (2003), No. 2, 225–264;Google Scholar

translation from Izv. Ross. Akad. Nauk Ser. Mat. 67 (2003), No. 2, 21–60.

[Kor2] M. A., Korolev, Sign change of the function S(t) on short intervals (English translation of Russian original), Izv. Math. 69 (2005), No. 4, 719–731;Google Scholar

translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69 (2005), No. 4, 75–88.

[Kor3] M. A., Korolev, On the primitive of the Hardy function Z(t), Dokl. Math. 75, No. 2, 295–298 (2007);Google Scholar

translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 413, No. 5, 599–602 (2007).

[Kor4] M. A., Korolev, On the integral of Hardy's function Z(t), Izv. Math. 72, No. 3, 429–478 (2008);Google Scholar

translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 3, 19–68 (2008).

[Kor5] M. A., Korolev, Gram's law and the argument of the Riemann zeta-function, to appear, preprint available at arXiv:1106.0516.

[Kos] H., Kösters, On the occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function, J. Number Theory 130 (2005), 2596–2609.Google Scholar

[Kra] E., Krätzel, Lattice Points, Mathematics and its Applications: East European Series, 33. Dordrecht, Kluwer Academic Publishers; Berlin: VEB Deutscher Verlag der Wissenschaften, 1988.

[Lan] E., Landau, Euler und Functionalgleichung der Riemannschen Zeta-Funktion, Biblio. Math.(3) Bd. 7, Leipzig, 1906, pp. 69–79.

[Lau1] A., Laurinčikas, On the zeta-function of Riemann on the critical line (Russian), Litovskij Mat. Sbornik 25 (1985), 114–118.Google Scholar

[Lau2] A., Laurinčikas, On the moments of the zeta-function of Riemann on the critical line (Russian), Mat. Zametki 39 (1986), 483–493.Google Scholar

[Lau3] A., Laurinčikas, The limit theorem for the Riemann zeta-function on the critical line I (Russian), Litovskij Mat. Sbornik 27 (1987), 113–132;Google Scholar

A., Laurinčikas, The limit theorem for the Riemann zeta-function on the critical line II (Russian), Litovskij Mat. Sbornik 27 (1987), 489–500.Google Scholar

[Lau4] A., Laurinčikas, A limit theorem for Dirichlet L-functions on the critical line (Russian), Litovskij Mat. Sbornik 27 (1987), 699–710.Google Scholar

[Lau5] A., Laurinčikas, Limit Theorems for the Riemann Zeta-Function, Kluwer, Dordrecht, 1996.

[Lau6] A., Laurinčikas, Limit theorems for the Mellin transforms of the Riemann zeta-function, Fiz. Mat. Fak. Moksl. Semin. Darb. 8 (2005), 63–75.Google Scholar

[Lav1] A. A., Lavrik, Uniform approximations and zeros of derivatives of Hardy's Z-function in short intervals (in Russian), Analysis Mathem. 17 (1991), 257–259.Google Scholar

[Lav2] A. A., Lavrik, Titchmarsh's problem in the discrete theory of the Riemann zeta-function. (English translation of Russian original)Proc. Steklov Inst. Math. 207 (1995), 179–209;Google Scholar

translation from Tr. Mat. Inst. Steklova 207 (1994), 197–230.

[Lavr] A. F., Lavrik, On the principal term in the divisor problem and power series of the Riemann zeta-function in a neighborhood of its pole (Russian), Trudy Mat. Inst. Steklova 142 (1976), 165–173, reprinted in Proc. Steklov Mat. Inst. 3 (1979), 175–183.Google Scholar

[LaIE] A. F., Lavrik, M. I., Israilov and Ž., Edgorov, On integrals containing the error term in the divisor problem (Russian), Acta Arith. 37 (1980), 381–389.Google Scholar

[LaTs] Y.-K., Lau and K.-M., Tsang, Omega result for the mean square of the Riemann zeta function, Manuscr. Math. 117 (2005), 373–381.Google Scholar

[Leh1] D. H., Lehmer, On the roots of the Riemann zeta function, Acta Math. 95 (1956), 291–298.Google Scholar

[Leh2] D. H., Lehmer, Extended computation of the Riemann zeta-function, Mathematika 3 (1956), 102–108.Google Scholar

[Lev] N., Levinson, More than one third of the zeros of Riemann's zeta-function are on σ = 1/2, Adv. Math. 18 (1975), 383–346.Google Scholar

[Lin] E., Lindelöf, Quelques remarques sur la croissance de la fonction ζ(s), Bull. Sci. Math. 32 (1908), 341–356.Google Scholar

[Lit] J. E., Littlewood, On the zeros of the Riemann zeta-function, Proc. Camb. Phil. Soc. 22 (1924), 295–318.Google Scholar

[Luk] M., Lukkarinen, The Mellin transform of the square of Riemann's zeta-function and Atkinson's formula, Doctoral Dissertation, Annales Acad. Sci. Fennicae, No. 140, Helsinki, 2005, 74 pp.

[LRW] J., van de Lune, H. J. J., te Riele and D. T., Winter, On the zeros of the Riemann zeta function in the critical strip. IV, Math. Comp. 46 (1986), 667–681.Google Scholar

[Man] H., von Mangoldt, Zu Riemann's Abhandlung “Über die Anzahl …,”, Crelle's J. 114 (1895), 255–305.Google Scholar

[MaTa] K., Matsumoto and Y., Tanigawa, On the zeros of higher derivatives of Hardy's Z-function, J. Number Theory 75 (1999), 262–278.Google Scholar

[Meh] M. L., Mehta, Random Matrices (3rd edn), Pure and Applied Mathematics, 142. Elsevier/Academic Press, Amsterdam, 2004.

[Mil] M. B., Milinovich, Moments of the Riemann zeta-function at its relative extrema on the critical line, Bull. London Math. Soc. 43 (2011), 1119–1129.Google Scholar

[Mol] G., Molteni, A note on a result of Bochner and Conrey-Ghosh about the Selberg class, Arch. Math. 72 (1999), 219–222.Google Scholar

[Mon1] H. L., Montgomery, The pair correlation of zeros of the zeta-function, in: Proc. Symp. Pure Math. 24, AMS, Providence, RI, 1973, 181–193.

[Mon2] H. L., Montgomery, Extreme values of the Riemann zeta-function, Comment. Math. Helv. 52 (1977), 511–518.Google Scholar

[MOd] H. L., Montgomery and A. M., Odlyzko, Gaps between zeros of the zeta function, in: Coll. Math. Soc. János Bolyai 34, Topics in Classical Number Theory (Budapest, 1981), 1079–1106.

[Mos1] J., Moser, The proof of the Titchmarsh hypothesis in the theory of the Riemann zeta-function (Russian), Acta Arith. 36 (1980), 147–156.Google Scholar

[Mos2] J., Moser, On the order of a sum of E. C. Titchmarsh in the theory of the Riemann zeta-function (Russian), Czech. Math. J. 41(116) (1991), 663–684.Google Scholar

[Mot1] Y., Motohashi, A note on the approximate functional equation for ζ2(s), Proc. Japan Acad. 59A (1983), 392–396,Google Scholar

Y., Motohashi, A note on the approximate functional equation for ζ2(s), II Proc. Japan Acad., 59A (1983), 469–472.Google Scholar

[Mot2] Y., Motohashi, Riemann-Siegel Formula, Lecture Notes, University of Colorado, Boulder, 1987.

[Mot3] Y., Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math. 170 (1993), 181–220.Google Scholar

[Mot4] Y., Motohashi, A relation between the Riemann zeta-function and the hyperbolic Laplacian, Annali Scuola Norm. Sup. Pisa, Cl. Sci. IV ser. 22 (1995), 299–313.Google Scholar

[Mot5] Y., Motohashi, Spectral Theory of the Riemann Zeta-Function, Cambridge University Press, Cambridge, 1997.

[Mot6] Y., Motohashi, The Riemann zeta-function and Hecke congruence subgroups II, Journal of Research Institute of Science and Technology, Tokyo, 2009, to appear.

[MoVa] H. L., Montgomery and R. C., Vaughan, Multiplicative Number Theory I. Classical Theory, Cambridge studies in advanced mathematics, Cambridge University Press, Cambridge, 2007.

[Mue] J., Mueller, On the difference between consecutive zeros of the Riemann zeta-function, J. Number Theory 14 (1982), 327–331.Google Scholar

[NaSt] H., Nagoshi and J., Steuding, Universality for L-functions in the Selberg class, Lithuanian Math. J. 50 (2010), 293–311.Google Scholar

[Odl1] A. M., Odlyzko, On the distribution of spacings between zeros of the zeta function, Math. Comp. 48 (1987), 273–308.Google Scholar

[Odl2] A. M., Odlyzko, The 1022-nd zero of the Riemann zeta function, in: M., van Frankenhuysen and M. L., Lapidus (eds.) Dynamical, Spectral, and Arithmetic Zeta Functions, Amer. Math. Soc., Contemporary Math. 290, 2001, 139–144.

[Odl3] A. M., Odlyzko, The 1020-th zero of the Riemann zeta-function and 175 million of its neighbors, unpublished, see www.dtc.umn.edu/~odlyzko/zeta_tables/index.html.

[Per] A., Perelli, A survey of the Selberg class of L-functions, Part I, Milan J. Math. 73 (2005), 19–52, and Part II, Riv. Mat. Univ. Parma 7 (2004), 83–118.Google Scholar

[Pia] I., Piatetski-Shapiro, Multiplicity one theorems, in: A., Borel and W., Casselman (eds.), Automorphic Forms, Representations and L-functions, Proc. Symp. Pure Math. 33, AMS Publications, 1979, 209–212.

[Pre] E., Preissmann, Sur la moyenne de la fonction zêta, in: K., Nagasaka (ed.) Analytic Number Theory and Related Topics, Proceedings of the Symposium, Tokyo, Japan, November 11–13, 1991, Singapore: World Scientific (1993), 119–125.

[Rad] M., Radziwill, The 4.36-th moment of the Riemann zeta-function, IMRN, to appear, preprint available at arXiv:1106.4806.

[RaSo] M., Radziwill and K., Soundararajan, Continuous lower bounds for moments of zeta and L-functions, preprint available at arXiv:1202.1351.

[Ram] K., Ramachandra, On the mean-value and omega-theorems for the Riemann zeta-function, LN's 85, Tata Inst. of Fundamental Research, Bombay, 1995 (Springer Verlag, Berlin).

[Ran] R. A., Rankin, Van der Corput's method and the theory of exponent pairs, Quart. J. Math. Oxford 6 (1955), 147–153.Google Scholar

[RaSa1] K., Ramachandra and A., Sankaranarayanan, Note on a paper by H.L. Montgomery-I, Publ. Inst. Math. 50 (64) (1991), 51–59.Google Scholar

[RaSa2] K., Ramachandra and A., Sankaranarayanan, On some theorems of Littlewood and Selberg I, J. Number Theory 44 (1993), 281–291.Google Scholar

[Ric] H.-E., Richert, Über Dirichlet Reihen mit Funktionalgleichung, Publs. Inst. Math. Serbe Sci. 1 (1957), 73–124.Google Scholar

[Rie] B., Riemann, Über die Anzahl der Primzahlen unter einer gegebener Grösse, Monatshefte Preuss. Akad. Wiss. (1859–1860), 671–680.

[RiLu] H. J. J., te Riele and J., van de Lune, Computational Number Theory at CWI in 1970–1994, CWI Quarterly 7(4) (1994), 285–335.Google Scholar

[Riv1] T., Rivoal, La fonction zêta de Riemann prend une infinitédevaleurs irrationnelles aux entiers impairs, C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 4 (2000), 267–270.Google Scholar

[Riv2] T., Rivoal, Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),…, ζ(21), Acta Arith. 103, No. 2 (2002), 157–167.Google Scholar

[RuYa] M. O., Rubinstein and S., Yamagishi, Computing the moment polynomials of the zeta function, to appear, preprint available at arXiv:1112.2201.

[Sar1] P., Sarnak, L-functions, in: Proc. International Congress of Mathematicians, Vol. I (Berlin, 1998), Doc. Math. 1998, Extra Vol. I, 453–465.

[Sar2] P., Sarnak, The grand Riemann hypothesis, Milan J. Math. 78 (2010), 61–63.Google Scholar

[Sel] A., Selberg, Selected Papers, Vol. I, Springer Verlag, Berlin 1989, and Vol. II, Springer Verlag, Berlin 1991.

[Sie] C. L., Siegel, Über Riemanns Nachlaß zur analytischen Zahlentheorie, Quell. Stud. Gesch. Mat. Astr. Physik 2 (1932), 45–80 (also in Gesammelte Abhandlungen, Band I, Springer Verlag, Berlin, 1966, 275–310).

[Sou1] K., Soundarajan, Omega results for the divisor and circle problems, Int. Math. Res. Not. 36 (2003), 1987–1998.Google Scholar

[Sou2] K., Soundarajan, Degree 1 elements of Selberg class, Expo. Math. 23 (2005), 65–70.Google Scholar

[Sou3] K., Soundarajan, Extreme values of zeta and L-functions, Math. Annalen 342 (2008), 467–486.Google Scholar

[Sou4] K., Soundarajan, Moments of the Riemann zeta function, Ann. Math. 170 (2010), 981–993.Google Scholar

[Spi] R., Spira, Some zeros of the Titchmarsh counterexample, Math. Comp. 63 (1994), 747–748.Google Scholar

[Sri] B. R., Srinivasan, Lattice point problems of many-dimensional hyperboloids II, Acta Arith. 8 (1963), 173–204, and II, Math. Annalen 160 (1965), 280–310.Google Scholar

[Ste] J., Steuding, Value-distribution of L-functions, Lecture Notes Math. 1877, Springer-Verlag, Berlin, 2007.

[Sti] T. J., Stieltjes, Correspondance d'Hermite et de Stieltjes, Tome 1, Gauthier-Villars, Paris, 1905.

[Sub] M. A., Subhankulov, Tauberian Theorems with Remainder Terms (Russian), Nauka, Moscow, 1976.

[Tit1] E. C., Titchmarsh, On van der Corput's method and the zeta-function of Riemann. IV, Quart. J. Math. 5 (1934), 98–105.Google Scholar

[Tit2] E. C., Titchmarsh, Introduction to the Theory of Fourier Integrals (2nd edn), Oxford University Press, Oxford, 1948.

[Tit3] E. C., Titchmarsh, The Theory of the Riemann Zeta-Function (2nd edn), Oxford University Press, Oxford, 1986.

[Tru1] T. S., Trudgian, Further results on Gram's law, DPhil Thesis, University of Oxford, Oxford, 2009, 95pp.

[Tru2] T. S., Trudgian, On the success and failure of Gram's law and the Rosser rule, Acta. Arith. 143 (2011), 225–256.Google Scholar

[Tru3] T. S., Trudgian, A modest improvement on the function S(T), to appear in Mathematics of Computation.

[Tsa1] K.-M., Tsang, Some Ω-theorems for the Riemann zeta-function, Acta Arith. 46 (1985), 369–395.Google Scholar

[Tsa2] K.-M., Tsang, The large values of the Riemann zeta-function, Mathematika 40 (1993), 203–214.

[Vin1] I. M., Vinogradov, Selected Works, Springer-Verlag, Berlin-New York, 1985.

[Vin2] I. M., Vinogradov, Method of Trigonometrical Sums in the Theory of Numbers, Dover Publications, Mineola, NY, 2004.

[Vor] S. M., Voronin, Theorem on the “universality” of the Riemann zeta-function (Russian), Izv. Akad. Nauk SSSR, Ser. Mat. 39 (1975), no. 3, 475–486.Google Scholar

[Wats] G. N., Watson, A Treatise on the Theory of Bessel Function (2nd edn), Cambridge University Press, Cambridge, 1952.

[Watt] N., Watt, A note on the mean square of ∣ζ(½ + it)∣, J. London Math. Soc. 82(2) (2010), 279–294.Google Scholar

[Wie] R., Wiebelitz, Über approximative Funktionalgleichungen der Potenzen der Riemannschen Zeta-funktion, Math. Nachr. 6 (1951–1952), 263–270.Google Scholar

[Wil] J. R., Wilton, An approximate functional equation for the product of two ζ-functions, Proc. London Math. Soc. 31 (1930), 11–17.Google Scholar

[Zud] V., Zudilin, Irrationality of values of the Riemann zeta function, Izv. Math. 66, No. 3 (2002), 489–542.Google Scholar

[You] M. P., Young, A short proof of Levinson's theorem, Arch. Math. 95 (2010), 539–548.Google Scholar