Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve

Vorrapan Chandee, Yoonbok Lee*, Sheng Chi Liu, Maksym Radziwiłł

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Assuming the generalized Riemann hypothesis, we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet L-functions are simple. This improves on earlier work of Özlük which gives a proportion of at most 86%. We further compute the q-analogue of the Pair Correlation Function F(α) averaged over all primitive Dirichlet L-functions in the range |α| < 2. Previously such a result was available only when the average included all the characters χ. As a corollary of our results, we obtain an asymptotic formula for a sum over characters similar to the one encountered in the Barban-Davenport-Halberstam Theorem.

Original languageEnglish (US)
Pages (from-to)63-87
Number of pages25
JournalQuarterly Journal of Mathematics
Volume65
Issue number1
DOIs
StatePublished - Mar 2014

ASJC Scopus subject areas

  • General Mathematics

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