Article ID Journal Published Year Pages File Type
4595478 Journal of Number Theory 2008 48 Pages PDF
Abstract

We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the zeta function whose spacing is three times larger than the average spacing. This is deduced from the calculation of the second moment of the Riemann zeta function multiplied by a Dirichlet polynomial averaged over the zeros of the zeta function.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory