A note on Linnik's approach to the Dirichlet L-functions

被引：1

作者：

Kaczorowski, J. ^{[1
,2
]}

Perelli, A. ^{[3
]}

机构：

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, Ul Umultowska 87, PL-61614 Poznan, Poland

[2] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

[3] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2017年 / 296卷 / 01期

关键词：

SELBERG CLASS; ZEROS;

D O I：

10.1134/S0081543817010096

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let chi (mod q), q > 1, be a primitive Dirichlet character. We first present a detailed account of Linnik's deduction of the functional equation of L(s, chi) from the functional equation of zeta(s). Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments.

引用

页码：115 / 124

页数：10

共 50 条

[31] SMALL ZEROS OF DIRICHLET L-FUNCTIONS
WEINBERGER, PJ
MATHEMATICS OF COMPUTATION, 1975, 29 (129) : 319 - 328
[32] DIRICHLET L-FUNCTIONS AND PRIMITIVE CHARACTERS
APOSTOL, TM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 31 (02) : 384 - &
[33] Dirichlet L-functions at the central point
Iwaniec, H
Sarnak, P
NUMBER THEORY IN PROGRESS, VOLS 1 AND 2: VOL 1: DIOPHANTINE PROBLEMS AND POLYNOMIALS; VOL 2: ELEMENTARY AND ANALYTIC NUMBER THEORY;, 1999, : 941 - 952
[34] On the Li coefficients for the Dirichlet L-functions
Mazhouda, Kamel
MONATSHEFTE FUR MATHEMATIK, 2013, 170 (3-4): : 405 - 423
[35] ON THE AVERAGE OF INVERSION OF DIRICHLET L-FUNCTIONS
ZHANG, WP
COMPOSITIO MATHEMATICA, 1992, 84 (01) : 53 - 57
[36] A converse theorem for Dirichlet L-functions
Kaczorowski, Jerzy
Molteni, Giuseppe
Perelli, Alberto
COMMENTARII MATHEMATICI HELVETICI, 2010, 85 (02) : 463 - 483
[37] Critical zeros of Dirichlet L-functions
Conrey, J. Brian
Iwaniec, Henryk
Soundararajan, Kannan
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 681 : 175 - 198
[38] FORMAL GROUPS AND DIRICHLET L-FUNCTIONS
KIM, JM
JOURNAL OF NUMBER THEORY, 1991, 37 (02) : 161 - 167
[39] Monotonicity results for Dirichlet L-functions
Dixit, Atul
Roy, Arindam
Zaharescu, Alexandru
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 410 (01) : 307 - 315
[40] COUNTING ZEROS OF DIRICHLET L-FUNCTIONS
Bennett, Michael A.
Martin, Greg
O'Bryant, Kevin
Rechnitzer, Andrew
MATHEMATICS OF COMPUTATION, 2021, 90 (329) : 1455 - 1482

← 1 2 3 4 5 →