Gaps between consecutive zeros of the zeta-function on the critical line and conjectures from random matrix theory

Abstract

Assuming the Riemann hypothesis and two conjectures from random matrix theory, we prove that $$\lambda = \limsup_{n \to \infty} (\gamma_{n+1} - \gamma_n) \frac{1}{2\pi} \log \frac{\gamma_n}{2\pi} = \infty.$$

Article information

Dates
Revised: 16 May 2006
First available in Project Euclid: 27 January 2019

https://projecteuclid.org/ euclid.aspm/1548550908

Digital Object Identifier
doi:10.2969/aspm/04910421

Mathematical Reviews number (MathSciNet)
MR2405613

Zentralblatt MATH identifier
1229.11115

Subjects
Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 15A52

Citation

Šleževičienė-Steuding, Rasa; Steuding, Jörn. Gaps between consecutive zeros of the zeta-function on the critical line and conjectures from random matrix theory. Probability and Number Theory — Kanazawa 2005, 421--432, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04910421. https://projecteuclid.org/euclid.aspm/1548550908