One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions
Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 427-454
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In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.
Mots-clés :
one level density, low-lying zero, quadratic Hecke character, quartic Hecke character, Hecke L-function
Gao, Peng; Zhao, Liangyi. One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions. Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 427-454. doi: 10.4153/S0008414X1900021X
@article{10_4153_S0008414X1900021X,
author = {Gao, Peng and Zhao, Liangyi},
title = {One-Level {Density} of {Low-lying} {Zeros} of {Quadratic} and {Quartic} {Hecke} $L$-functions},
journal = {Canadian journal of mathematics},
pages = {427--454},
year = {2020},
volume = {72},
number = {2},
doi = {10.4153/S0008414X1900021X},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X1900021X/}
}
TY - JOUR AU - Gao, Peng AU - Zhao, Liangyi TI - One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions JO - Canadian journal of mathematics PY - 2020 SP - 427 EP - 454 VL - 72 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X1900021X/ DO - 10.4153/S0008414X1900021X ID - 10_4153_S0008414X1900021X ER -
%0 Journal Article %A Gao, Peng %A Zhao, Liangyi %T One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions %J Canadian journal of mathematics %D 2020 %P 427-454 %V 72 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X1900021X/ %R 10.4153/S0008414X1900021X %F 10_4153_S0008414X1900021X
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