On large gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions

Bredberg, Johan

doi:10.48550/arxiv.1003.2290

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2012

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“…Also, for large gaps, Hall has invented a method that gives unconditional results. [Bre1] and [Bre2] has recently used Hall's method to show that the Riemann zeta-function has gaps between consecutive zeros as large as 2.766 times the average, and in conjunction with [CSI1] to prove the existence of Dirichlet L-functions with gaps as large as 3.54 times the average.…”

Section: Statement Of Resultsmentioning

confidence: 99%

Small gaps between zeros of twisted L-functions

2012

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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.. Dedicated to Professor Andrzej Schinzel on his 75-th birthday 2010 Mathematics Subject Classification. Primary 11M26.

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Section: Statement Of Resultsmentioning

confidence: 99%