Simultaneous non-vanishing for Dirichlet L-functions

2017/06/14 by Raphaël Zacharias, Zacharias, Raphael · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1706.04888

openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the work of Fouvry, Kowalski and Michel on correlation between Hecke eigenvalues of modular forms and algebraic trace functions in order to establish an asymptotic formula for a generalized cubic moment of modular L-functions at the central point s = 1/2 and for prime moduli q. As an application, we exploit our recent result on the mollification of the fourth moment of Dirichlet L-functions to derive that for any pair (ω₁,ω₂) of multiplicative characters modulo q, there is a positive proportion of χ (mod q) such that L(χ, 1/2 ), L(χω₁, 1/2 ) and L(χω₂, 1/2) are simultaneously not too small.

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