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 $$ \lambda = \limsup_{n \to \infty} (\gamma_{n+1} - \gamma_n) \frac{1}{2\pi} \log \frac{\gamma_n}{2\pi} = \infty. $$