Journal title
Journal of the European Mathematical Society
DOI
10.4171/JEMS/1084
Issue
2
Volume
24
Last updated
2023-08-01T04:04:20.517+01:00
Page
369-460
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 Riemann Hypothesis, we show that our lower bound for the second moment is asymptotically sharp.
Symplectic ID
1159059
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Publication type
Journal Article
Publication date
20 Jul 2021