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

Cech Martin; Matomäki Kaisa
A note on exceptional characters and non-vanishing of Dirichlet L-functions

Cech Martin
Matomäki Kaisa
Katso/Avaa
Lataukset: 

SPRINGER HEIDELBERG
doi:10.1007/s00208-023-02667-x
URI
https://link.springer.com/article/10.1007/s00208-023-02667-x
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Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2025082789324
Tiivistelmä

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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