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• W2893562135 abstract "We prove that more than nine percent of the central values $L(frac{1}{2},chi_p)$ are non-zero, where $pequiv 1 pmod{8}$ 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 $L(frac{1}{2},chi_p)$, 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." @default.
• W2893562135 created "2018-10-05" @default.
• W2893562135 creator A5005422405 @default.
• W2893562135 creator A5064132642 @default.
• W2893562135 date "2018-09-26" @default.
• W2893562135 modified "2023-10-10" @default.
• W2893562135 title "Dirichlet $L$-functions of quadratic characters of prime conductor at the central point" @default.
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