Large gaps between the zeros of the Riemann zeta function

Details Large gaps between the zeros of the Riemann zeta function Large gaps between the zeros of the Riemann zeta function

2005-10-25

arxiv.org/abs/math/0510530v1

Mathematics

Number Theory

39 pages

Scientific paper

We show that the generalized Riemann hypothesis implies that there are
infinitely many consecutive zeros of the Riemann zeta function whose spacing is
2.9125 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.

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