THE EIGHTH MOMENT OF DIRICHLET L-FUNCTIONS II

被引：0

作者：

Chandee, Vorrapan ^{[1
]}

Li, Xiannan ^{[1
]}

Matomaki, Kaisa ^{[2
]}

Radziwill, Maksym ^{[3
]}

机构：

[1] Kansas State Univ, Math Dept, Manhattan, KS 66506 USA

[2] Univ Turku, Dept Math & Stat, Turku, Finland

[3] Northwestern Univ, Dept Math, Evanston, IL USA

来源：

DUKE MATHEMATICAL JOURNAL | 2024年 / 173卷 / 18期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

POWER MOMENT;

D O I：

10.1215/00127094-2024-0014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove an asymptotic formula for the eighth moment of Dirichlet L-functions averaged over primitive characters x modulo q, over all moduli q Q, and with a short average on the critical line. Previously the same result was shown conditionally on the generalized Riemann hypothesis by the first two authors.

引用

页码：3453 / 3493

页数：41

共 12 条

[1]

Chandee V, 2024, Arxiv, DOI arXiv:2409.01457

[2] The eighth moment of Dirichlet L-functions [J].

Chandee, Vorrapan ;

Li, Xiannan .

ADVANCES IN MATHEMATICS, 2014, 259 :339-375

[3] The Sixth Power Moment of Dirichlet L-Functions [J].

Conrey, J. B. ;

Iwaniec, H. ;

Soundararajan, K. .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2012, 22 (05) :1257-1288

[4] Integral moments of L-functions [J].

Conrey, JB ;

Farmer, DW ;

Keating, JP ;

Rubinstein, MO ;

Snaith, NC .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 :33-104

[5]

Fortes M., 1949, The Theory of the Riemann Zeta-Function

[6]

Harman G., 2007, Prime-detecting sieves, V33

[7] 12TH POWER MOMENT OF THE RIEMANN-FUNCTION [J].

HEATHBROWN, DR .

QUARTERLY JOURNAL OF MATHEMATICS, 1978, 29 (116) :443-462

[8]

Iwaniec Henryk., 2004, Analytic Number Theory, V53, DOI DOI 10.1090/COLL/053

[9]

RAMACHANDRA K, 1975, J LOND MATH SOC, V10, P482

[10]

RICHERT H.E., 1976, Tata Institute of Fundamental Research Lectures on Mathematics, V55

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