Moments and zero density estimates for Dirichlet L-functions

被引：0
作者：
Sono, Keiju [1 ]
机构：
[1] Kobe Univ, Dept Math, Kobe, Hyogo, Japan
来源：
TURKISH JOURNAL OF MATHEMATICS | 2021年 / 45卷 / 05期
关键词：
Dirichlet L-functions; Riemann zeta-function; zero density estimate; POWER MOMENT; LARGE VALUES;
D O I：
10.3906/mat-2104-29
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we estimate the density of zeros of primitive Dirichlet L-functions in the half-plane R(s) > 1/2, under the assumption of a plausible conjecture on high moments of Dirichlet L-functions on the critical line. We conditionally improve the results of Huxley [9], Jutila [13], Heath-Brown [5, 6] and Bourgain [1].
引用
收藏
页码：2050 / 2072
页数：23
相关论文
共 18 条
[11]   NOTE ON THE ZERO-DENSITY ESTIMATES FOR THE ZETA FUNCTION [J].
IVIC, A .
ARCHIV DER MATHEMATIK, 1979, 33 (02) :155-164
[12]  
Ivic A., 1985, RIEMANN ZETA FUNCTIO
[13]  
Jutila M., 1977, Acta Arith., V32, P55
[14]   MEAN AND LARGE VALUES OF DIRICHLET POLYNOMIALS [J].
MONTGOMERY, HL .
INVENTIONES MATHEMATICAE, 1969, 8 (04) :334-+
[15]  
Montgomery HughL, Lect. Notes Math, V227, DOI DOI 10.1007/BFB0060851
[16]  
Ramachandra K., 1975, Ann. Acad. Sci. Fenn. Ser. A I Math., V1, P177
[17]   Moments of the Riemann zeta function [J].
Soundararajan, Kannan .
ANNALS OF MATHEMATICS, 2009, 170 (02) :981-993
[18]   A conditional density theorem for the zeros of the Riemann zeta-function [J].
Zaccagnini, A .
ACTA ARITHMETICA, 2000, 93 (03) :293-301
12