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arXiv · 1710.04909

Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$

Peng Gao·Liangyi Zhao
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Abstract

In this paper, we evaluate explicitly certain quadratic Hecke Gauss sums of $\mathbb{Q}(ω), ω=\exp \left( \frac {2πi}{3}\right)$. As applications, we study the moments of central values of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$, and establish quantitative non-vanishing result for the $L$-values. We also establish an one level density result for the low-lying zeros of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$.

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Peng Gao, Liangyi Zhao. 2019-08-20. Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$. https://arxiv.org/abs/1710.04909

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