Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T02:46:38.467Z Has data issue: false hasContentIssue false
  • English
  • Français

A JOINT UNIVERSALITY THEOREM FOR PERIODIC HURWITZ ZETA-FUNCTIONS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  01 August 2008

A. JAVTOKAS  and
A. LAURINČIKAS
A. JAVTOKAS
Affiliation:
Department of Math. and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania (email: [email protected])
A. LAURINČIKAS*
Affiliation:
Department of Math. and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove a joint universality theorem in the Voronin sense for the periodic Hurwitz zeta-functions.

Keywords

Hurwitz zeta-functionsprobability measureuniversalityweak convergence

MSC classification

Secondary: 11M35: Hurwitz and Lerch zeta functions 11M41: Other Dirichlet series and zeta functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 13 - 33
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Bagchi, B., ‘The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series’, PhD Thesis, Indian Statistical Institute, Calcutta, 1981.Google Scholar
[2]Bagchi, B., ‘Joint universality theorem for Dirichlet L-functions’, Math. Z. 181 (1982), 319–334.CrossRefGoogle Scholar
[3]Billingsley, P., Convergence of Probability Measures (J. Wiley & Sons, New York, 1968).Google Scholar
[4]Genys, J. and Laurinčikas, A., ‘Value distribution of general Dirichlet series’, Liet. Mat. Rink. 44(2) (2004), 181–195 (in Russian); Lithuanian Math. J. 44(2) (2004), 145–156.Google Scholar
[5]Gonek, S. M., ‘Analytic properties of zeta and L-functions’, PhD Thesis, University of Michigan, 1979.Google Scholar
[6]Grosse-Erdmann, K.-G., ‘Universal families and hypercyclic operators’, Bull. Amer. Math. Soc. 36 (1999), 345–381.CrossRefGoogle Scholar
[7]Heyer, H., Probability Measures on Locally Compact Groups (Springer, Berlin, 1977).CrossRefGoogle Scholar
[8]Javtokas, A. and Laurinčikas, A., ‘On the periodic Hurwitz zeta-function’, Hardy-Ramanujan J. 29 (2006), 18–36.Google Scholar
[9]Javtokas, A. and Laurinčikas, A., ‘The universality of the periodic Hurwitz zeta-function’, Integral Transforms Spec. Funct. 17(10) (2006), 711–722.CrossRefGoogle Scholar
[10]Laurinčikas, A., Limit Theorems for the Riemann Zeta-function (Kluwer Academic, Dordrecht, 1996).CrossRefGoogle Scholar
[11]Laurinčikas, A., ‘On the zeros of linear combinations of Matsumoto zeta-functions’, Liet. Mat. Rink. 38 (1998), 185–204 (in Russian). Lithuanian. Math. J. 38 (1998), 144–159.Google Scholar
[12]Laurinčikas, A., ‘The joint universality for general Dirichlet series’, Ann. Univ. Sci. Budapest. Sect. Comput. 22 (2003), 235–251.Google Scholar
[13]Laurinčikas, A., ‘The universality of zeta-functions’, Acta Appl. Math. 78 (2003), 251–271.CrossRefGoogle Scholar
[14]Laurinčikas, A., ‘The joint universality of Dirichlet series’, Proc. Sci. Seminar Faculty of Physics and Math., Šiauliai Univ. 7 (2004), 33–44.Google Scholar
[15]Laurinčikas, A., ‘The joint universality for periodic Hurwitz zeta-functions’, Analysis 26 (2006), 419–428.CrossRefGoogle Scholar
[16]Laurinčikas, A., ‘The Voronin-type theorem for periodic Hurwitz zeta-functions’, Sb. Math. 198(1–2) (2007), 231–242.CrossRefGoogle Scholar
[17]Laurinčikas, A. and Garunkštis, R., The Lerch Zeta-function (Kluwer Academic, Dordrecht, 2002).Google Scholar
[18]Laurinčikas, A. and Matsumoto, K., ‘The joint universality and the functional independence for Lerch zeta-functions’, Nagoya Math. J. 157 (2000), 211–227.CrossRefGoogle Scholar
[19]Laurinčikas, A. and Matsumoto, K., ‘The joint universality of zeta-functions attached to certain cusp forms’, Proc. Sci. Seminar Faculty of Physics and Math., Šiauliai Univ. 5 (2002), 58–75.Google Scholar
[20]Laurinčikas, A. and Matsumoto, K., ‘The joint universality of twisted automorphic L-functions’, J. Math. Soc. Japan 56(3) (2004), 923–939.CrossRefGoogle Scholar
[21]Matsumoto, K., ‘Probabilistic value-distribution theory of zeta functions’, Sugaku Expositions 17(1) (2004), 51–71.Google Scholar
[22]Steuding, J., Value-distribution of L-functions, Lecture Notes in Mathematics, 1877 (Springer, Berlin, 2007).Google Scholar
[23]Šleževičienė, R., ‘The joint universality for twists of Dirichlet series with multiplicative coefficients’, in: Analytic and Probability Methods in Number Theory, Proc. 3rd Int. Conf. in Honor of J. Kubilius, Palanga, 2001 (eds. A. Dubickas et al.) (TEV, Vilnius, 2002), pp. 303–319.Google Scholar
[24]Voronin, S. M., ‘Theorem on the universality of the Riemann zeta-function’, Math. USSR Izv. 9 (1975), 443–453.CrossRefGoogle Scholar
[25]Voronin, S. M., ‘On the functional independence of Dirichlet L-functions’, Acta Arith. 27 (1975), 493–503 (in Russian).Google Scholar
[26]Walsh, J. L., ‘Interpolation and approximation by rational functions in the complex domain’, Amer. Math. Soc. Colloq. Publ. 20 (1960).Google Scholar