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- Title
A note on exceptional characters and non-vanishing of Dirichlet L-functions.
- Authors
Čech, Martin; Matomäki, Kaisa
- 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 ∈ [ D 300 , D O (1) ] , one has L (1 / 2 , χ) ≠ 0 for almost all Dirichlet characters χ (mod q) .
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 1, p987
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02667-x