Abstract
The generalized Riemann hypothesis implies that at least 50% of the central values are nonvanishing as ranges over primitive characters modulo . We show that one may unconditionally go beyond GRH, in the sense that if one averages over primitive characters modulo and averages over an interval, then at least 50.073% of the central values are nonvanishing. The proof utilizes the mollification method with a three-piece mollifier, and relies on estimates for sums of Kloosterman sums due to Deshouillers and Iwaniec.
Citation
Kyle Pratt. "Average nonvanishing of Dirichlet $L$-functions at the central point." Algebra Number Theory 13 (1) 227 - 249, 2019. https://doi.org/10.2140/ant.2019.13.227
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