Moments and Non-vanishing of central values of Quadratic Hecke L-functions in the Gaussian Field

2020/02/27 by Peng Gao, Gao, Peng
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2002.11899

25 pages

arxiv created 2020/02/27 · arxiv updated 2020/02/28

Abstract

We evaluate the first three moments of central values of a family of qudratic Hecke L-functions in the Gaussian field with power saving error terms. In particular, we obtain asymptotic formulas for the first two moments with error terms of size O(X^1/2+ε). We also study the first and second mollified moments of the same family of L-functions to show that at least 87.5% of the members of this family have non-vanishing central values.

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