MOMENTS AND ONE LEVEL DENSITY OF SEXTIC HECKE L-FUNCTIONS

Peng Gao; Liangyi Zhao

doi:10.7169/facm/2057

MOMENTS AND ONE LEVEL DENSITY OF SEXTIC HECKE L-FUNCTIONS

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

University of New South Wales

Research output: Contribution to journal › Article › peer-review

Abstract

Let ω = exp(2πi/3). In this paper, we study moments of central values of sextic Hecke L-functions of Q(ω) and one level density result for the low-lying zeros of sextic Hecke L-functions of Q(ω). 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.

Original language	English
Pages (from-to)	7-28
Number of pages	22
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	70
Issue number	1
DOIs	https://doi.org/10.7169/facm/2057
State	Published - Mar 2024

Keywords

Hecke L-functions
low-lying zeros
one level density
sextic Hecke characters

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abstract = "Let ω = exp(2πi/3). In this paper, we study moments of central values of sextic Hecke L-functions of Q(ω) and one level density result for the low-lying zeros of sextic Hecke L-functions of Q(ω). 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.",

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AB - Let ω = exp(2πi/3). In this paper, we study moments of central values of sextic Hecke L-functions of Q(ω) and one level density result for the low-lying zeros of sextic Hecke L-functions of Q(ω). 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.

KW - Hecke L-functions

KW - low-lying zeros

KW - one level density

KW - sextic Hecke characters

UR - https://www.scopus.com/pages/publications/85188191768

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JF - Functiones et Approximatio, Commentarii Mathematici

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ER -

MOMENTS AND ONE LEVEL DENSITY OF SEXTIC HECKE L-FUNCTIONS

Abstract

Keywords

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