Critical zeros of Dirichlet L-functions

2011/05/05 by Conrey, Brian, Iwaniec, Henryk, Soundararajan, Kannan
#11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1105.1177

Abstract

We use the Asymptotic Large Sieve and Levinson's method to obtain lower bounds for the proportion of simple zeros on the critical line of the twists by primitive Dirichlet characters of a fixed L-function of degree 1,2, or 3.

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• Zeros of Dirichlet L-functions on the critical line
• Zeros of linear combinations of Dirichlet L-functions on the critical line
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• Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve