A1 Refereed original research article in a scientific journal

A note on exceptional characters and non-vanishing of Dirichlet L-functions



Authors: Cech Martin, Matomäki Kaisa

Publisher: SPRINGER HEIDELBERG

Publication year: 2023

Journal: Mathematische Annalen

Journal name in source: MATHEMATISCHE ANNALEN

Journal acronym: MATH ANN

Number of pages: 10

ISSN: 0025-5831

eISSN: 1432-1807

DOI: https://doi.org/10.1007/s00208-023-02667-x

Web address : https://link.springer.com/article/10.1007/s00208-023-02667-x

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/180427980


Abstract

We study non-vanishing of Dirichlet L-functions at the central point under the unlikely assumption that there exists an exceptional Dirichlet character. In particular we prove that if ψ is a real primitive character modulo D ∈ N with L(1,ψ) ≪ (log D)−25−ε, then, for any prime q ∈ [D300, DO(1)], one has L(1/2, χ) ≠ 0 for almost all Dirichlet characters χ (mod q).


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Last updated on 2024-26-11 at 14:58