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arXiv · 1708.01701

One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions

Peng Gao·Liangyi Zhao
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Abstract

In this paper, we prove some one level density results for the low-lying zeros of famliies of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that, respectively, at least $94.27 \%$ and $5\%$ of the members of the quadratic family and the quartic family do not vanish at the central point.

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Peng Gao, Liangyi Zhao. 2017-08-05. One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions. https://arxiv.org/abs/1708.01701

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