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Dirichlet L-functions of quadratic characters of prime conductor at the central point

Abstract:

We prove that more than nine percent of the central values $L(1/2,\chi_p)$ are non-zero, where $p\equiv 1 \pmod{8}$ ranges over primes and $\chi_p$ is the real primitive Dirichlet character of conductor $p$. Previously, it was not known whether a positive proportion of these central values are non-zero. As a by-product, we obtain the order of magnitude of the second moment of $L(1/2,\chi_p)$, and conditionally we obtain the order of magnitude of the third moment. Assuming the Generalized Riem...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/JEMS/1084

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
European Mathematical Society
Journal:
Journal of the European Mathematical Society More from this journal
Volume:
24
Issue:
2
Pages:
369-460
Publication date:
2021-07-20
Acceptance date:
2020-10-27
DOI:
EISSN:
1435-9863
ISSN:
1435-9855
Language:
English
Keywords:
Pubs id:
1159059
Local pid:
pubs:1159059
Deposit date:
2021-01-29

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