Bounds for moments of Dirichlet L-functions to a fixed modulus

Peng Gao

doi:10.1007/s00209-024-03541-5

Bounds for moments of Dirichlet L-functions to a fixed modulus

Peng Gao^*

^*Corresponding author for this work

School of Mathematical Sciences

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

1 Scopus citations

Abstract

We study the 2k-th moment of central values of the family of Dirichlet L-functions to a fixed prime modulus. We establish sharp lower bounds for all real k≥0 and sharp upper bounds for k in the range 0≤k≤1.

Original language	English
Article number	70
Journal	Mathematische Zeitschrift
Volume	307
Issue number	4
DOIs	https://doi.org/10.1007/s00209-024-03541-5
State	Published - Aug 2024

Keywords

11M06
Dirichlet L-functions
Lower bounds
Moments
Upper bounds

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10.1007/s00209-024-03541-5

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title = "Bounds for moments of Dirichlet L-functions to a fixed modulus",

abstract = "We study the 2k-th moment of central values of the family of Dirichlet L-functions to a fixed prime modulus. We establish sharp lower bounds for all real k≥0 and sharp upper bounds for k in the range 0≤k≤1.",

keywords = "11M06, Dirichlet L-functions, Lower bounds, Moments, Upper bounds",

author = "Peng Gao",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

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AB - We study the 2k-th moment of central values of the family of Dirichlet L-functions to a fixed prime modulus. We establish sharp lower bounds for all real k≥0 and sharp upper bounds for k in the range 0≤k≤1.

KW - 11M06

KW - Dirichlet L-functions

KW - Lower bounds

KW - Moments

KW - Upper bounds

UR - https://www.scopus.com/pages/publications/85197794815

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DO - 10.1007/s00209-024-03541-5

M3 - 文章

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VL - 307

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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M1 - 70

ER -

Bounds for moments of Dirichlet L-functions to a fixed modulus

Abstract

Keywords

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