Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T01:24:53.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Large gaps between zeros of the zeta-function

Published online by Cambridge University Press:  26 February 2010

J. B. Conrey ,
A. Ghosh  and
S. M. Gonek
J. B. Conrey
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA.
A. Ghosh
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA.
S. M. Gonek
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA.
Get access

Extract

Let 0 < γ ≤ γ” denote the ordinates of consecutive nontrivial zeros of ζ(s) and set

Type
Research Article
Information
Mathematika , Volume 33 , Issue 2 , December 1986 , pp. 212 - 238
Copyright
Copyright © University College London 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Balasubramanian, R., Conrey, J. B. and Heath-Brown, D. R.. Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. J. Reine Angew. Math., 357 (1985), 161–181.Google Scholar
2.Conrey, J. B., Ghosh, A. and Gonek, S. M.. A note on gaps between zeros of the zeta-function. Bull. London Math. Soc., 16 (1984) 421–424.CrossRefGoogle Scholar
3.Conrey, J. B., Ghosh, A. and Gonek, S. M.. Simple zeros of the Riemann zeta-function. To be submitted.Google Scholar
4.Davenport, H.. Multiplicative Number Theory, 2nd edition (Berlin, Springer, 1980).CrossRefGoogle Scholar
5.Estermann, T.. On the representation of a number as the sum of two products. Proc. London Math. Soc. (2), 31 (1930), 123–133.CrossRefGoogle Scholar
6.Fujii, A.. On the difference between r consecutive ordinates of the zeros of the Riemann zeta function. Proc. Japan Acad., 51 (1975), 741–743.Google Scholar
7.Gonek, S. M.. Mean values of the Riemann zeta-function and its derivatives. Inventiones Math., 75 (1984), 123–141.CrossRefGoogle Scholar
8.Montgomery, H.L.. The pair correlation of zeros of the zeta function. Proc. Symp. Pure Math., A.M.S. Providence, 24 (1973), 181–193.CrossRefGoogle Scholar
9.Montgomery, H. L. and Odlyzko, A.. Gaps between zeros of the zeta function. Topics in Classical Number Theory, Colloquia Math. Soc. Janos Bolyai, 34 (Budapest, 1981).Google Scholar
10.Mueller, J.. On the difference between consecutive zeros of the Riemann zeta function. J. of Number Theory, 14 (1982), 327–331.CrossRefGoogle Scholar
11.Selberg, A.. The zeta-function and the Riemann hypothesis. Skandinaviske Mathematikerkongres, 10 (1946), 187–200.Google Scholar
12.Titchmarsh, E. C.. The Theory of the Riemann Zeta-Function (Oxford, Oxford University Press, 1951).Google Scholar
13.Whittaker, E. T. and Watson, G. N.. A Course of Modern Analysis (Cambridge, Cambridge University Press, 1969).Google Scholar