Large gaps between zeros of the zeta‐function

A note on the gaps between consecutive zeros of the Riemann zeta-function

“…The results in Hall's paper are actually unconditional, but a lower bound for λ can only be obtained if the Riemann Hypothesis is assumed. Assuming the generalized Riemann Hypothesis for the zeros of Dirichlet L-functions, Conrey, Ghosh, and Gonek [3] have shown that λ > 2.68. Their method can be modified (see [11] and [1]) to show that λ > 3.…”

A Wirtinger Type Inequality and the Spacing of the Zeros of the Riemann Zeta-Function

“…Assuming the Riemann Hypothesis, Montgomery and Odlyzko [12] proved that l \ 1.9799 and this lower bound was improved to l > 2.337 by Conrey et al [4]. Later these authors [5] obtained the bound l > 2.68 assuming the Generalized Riemann Hypothesis. My main objective here is to make a slight improvement in the constant on the right-hand side of (4).…”

“…The not larger quantity l :=lim sup c n+1 − c n (2p/log c n ) (5) in which {c n } denotes the sequence of ordinates of all the zeros b n +ic n in the upper half-plane (labelled in such a way that c n is non-decreasing), is known to exceed 1 (Selberg [13]). Assuming the Riemann Hypothesis, Montgomery and Odlyzko [12] proved that l \ 1.9799 and this lower bound was improved to l > 2.337 by Conrey et al [4].…”

The Riemann zeta-function and moment conjectures from Random Matrix Theory

“…Under assumption of the generalized Riemann hypothesis C o n r e y , G h o s h & G o n e k [5] obtained an asymptotic formula for…”