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Large gaps between zeros of the zeta-function

Published online by Cambridge University Press:  26 February 2010

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.
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Extract

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

Type
Research Article
Copyright
Copyright © University College London 1986

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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), 161181.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) 421424.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), 123133.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), 741743.Google Scholar
7.Gonek, S. M.. Mean values of the Riemann zeta-function and its derivatives. Inventiones Math., 75 (1984), 123141.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), 181193.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), 327331.CrossRefGoogle Scholar
11.Selberg, A.. The zeta-function and the Riemann hypothesis. Skandinaviske Mathematikerkongres, 10 (1946), 187200.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