Small gaps between zeros of twisted L-functions

Details Small gaps between zeros of twisted L-functions Small gaps between zeros of twisted L-functions

2012-02-13

arxiv.org/abs/1202.2671v1

Mathematics

Number Theory

19 pages; to appear in Acta Arithmetica

Scientific paper

We use the asymptotic large sieve, developed by the authors, to prove that if the Generalized Riemann Hypothesis is true, then there exist many Dirichlet L-functions that have a pair of consecutive zeros closer together than 0.37 times their average spacing. More generally, we investigate zero spacings within the family of twists by Dirichlet characters of a fixed L-function and give precise bounds for small gaps which depend only on the degree of the L-function.

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