BOUNDS FOR MOMENTS OF QUADRATIC DIRICHLET L-FUNCTIONS OF PRIME-RELATED MODULI

Peng Gao; Liangyi Zhao

doi:10.4064/cm8650-1-2022

BOUNDS FOR MOMENTS OF QUADRATIC DIRICHLET L-FUNCTIONS OF PRIME-RELATED MODULI

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

University of New South Wales

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

4 Scopus citations

Abstract

We study the kth moment of central values of the family of quadratic Dirichlet L-functions of moduli 8p, with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the kth power moment of these L-values for all real k ≥ 0.

Original language	English
Pages (from-to)	61-77
Number of pages	17
Journal	Colloquium Mathematicum
Volume	171
Issue number	1
DOIs	https://doi.org/10.4064/cm8650-1-2022
State	Published - 2023

Keywords

lower bounds
moments
prime moduli
quadratic Dirichlet L-functions
upper bounds

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10.4064/cm8650-1-2022

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abstract = "We study the kth moment of central values of the family of quadratic Dirichlet L-functions of moduli 8p, with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the kth power moment of these L-values for all real k ≥ 0.",

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AU - Zhao, Liangyi

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PY - 2023

Y1 - 2023

N2 - We study the kth moment of central values of the family of quadratic Dirichlet L-functions of moduli 8p, with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the kth power moment of these L-values for all real k ≥ 0.

AB - We study the kth moment of central values of the family of quadratic Dirichlet L-functions of moduli 8p, with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the kth power moment of these L-values for all real k ≥ 0.

KW - lower bounds

KW - moments

KW - prime moduli

KW - quadratic Dirichlet L-functions

KW - upper bounds

UR - https://www.scopus.com/pages/publications/85139816433

U2 - 10.4064/cm8650-1-2022

DO - 10.4064/cm8650-1-2022

M3 - 文章

AN - SCOPUS:85139816433

SN - 0010-1354

VL - 171

SP - 61

EP - 77

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 1

ER -

BOUNDS FOR MOMENTS OF QUADRATIC DIRICHLET L-FUNCTIONS OF PRIME-RELATED MODULI

Abstract

Keywords

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