Hostname: page-component-784d4fb959-mv4gh Total loading time: 0 Render date: 2025-07-14T15:56:56.412Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Unconditional Result about Large Spaces Between Zeta Zeros

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

Published online by Cambridge University Press:  21 December 2009

R. R. Hall
R. R. Hall
Affiliation:
Mathematics Department, York University, York YO10 5DDUnited Kingdom.
Get access

Extract

Suppose that {tn} is the sequence of positive roots of ζ (½ + it) counted according to multiplicity and arranged in non-decreasing order; in my paper [6] I proved that

and my main objective here is to improve this bound.

MSC classification

Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses

Information

Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 101 - 113
Copyright
Copyright © University College London 2005

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.)

Article purchase

Temporarily unavailable

References

1Conrey, 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
2Conrey, J. B., Ghosh, A. and Gonek, S. M., Large gaps between zeros of the zeta-function. Mathematika 33 (1986), 212–238.CrossRefGoogle Scholar
3Conrey, J. B., The fourth moment of derivatives of the Riemann zeta-function: Quart. J. Math. Oxford Ser. (2) 39 (1988), 21–36.CrossRefGoogle Scholar
4Edwards, H. M., Riemann's Zeta-Function. Academic Press (New York) 1974.Google Scholar
5Hall, R. R., The behaviour of the Riemann zeta-function on the critical line. Mathematika 46 (1999), 281–313.CrossRefGoogle Scholar
6Hall, R. R., A Wirtinger type inequality and the spacing of the zeros of the Riemann zeta-function. J. Number Theory 93 (2002), 235–245.CrossRefGoogle Scholar
7Hall, R. R., On the stationary points of Hardy's function Z(t). Acta Arithmetica 111 (2004), 125–140.CrossRefGoogle Scholar
8Hall, R. R. and Tenenbaum, G., Divisors. Cambridge Tracts in Mathematics No. 90 (Cambridge 1988).Google Scholar
9Hardy, G. H. and Littlewood, J. E., Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes. Acta Math. 41 (1918), 119–196.CrossRefGoogle Scholar
10Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities. (Cambridge, 1934).Google Scholar
11Ingham, A. E., Mean-value theorems in the theory of the Riemann zeta-function. Proc. London Math. Soc. (2) 27 (1928), 273–300.CrossRefGoogle Scholar
12Montgomery, H. L. and Odlyzko, A. M., Gaps between zeros of the zeta-function. Coll. Math. Soc. János Bolyai 34. Topics in Classical Number Theory (Budapest, 1981).Google Scholar
13Motohashi, Y., A note on the approximate functional equation for ζ2(s). Proc. Japan Acad. Ser. A 59 (1983), 393–396.Google Scholar
14Mueller, J., On the difference between consecutive zeros of the Riemann zeta-function. J. Number Theory 14 (1982), 327–331.CrossRefGoogle Scholar
15Selberg, A., The zeta-function and the Riemann Hypothesis. Skandinaviske Mathematikerkongres 10 (1946), 187–200.Google Scholar
16Titchmarsh, E. C., The theory of the Riemann zeta-function (revised by Heath-Brown, D.R.) (Oxford, 1986).Google Scholar
17Wilton, J. R., An approximate functional equation for the product of two ζ-functions. Proc. London Math. Soc. 31 (1930), 11–17.CrossRefGoogle Scholar