Abstract
Let $\omega = \exp (2\pi i/3)$. In this paper, we study moments of central values of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$ and one level density result for the low-lying zeros of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$. As a corollary, we deduce that, assuming GRH, at least $2/45$ of the members of the sextic family do not vanish at $s=1/2$.
Citation
Peng Gao. Liangyi Zhao. "Moments and one level density of sextic Hecke $L$-functions." Funct. Approx. Comment. Math. 70 (1) 7 - 28, March 2024. https://doi.org/10.7169/facm/2057
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