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

被引：0
|
作者：
J. Kaczorowski
A. Perelli
机构：
[1] Adam Mickiewicz University,Faculty of Mathematics and Computer Science
[2] Institute of Mathematics of the Polish Academy of Sciences,Dipartimento di Matematica
[3] Università di Genova,undefined
来源：
Proceedings of the Steklov Institute of Mathematics | 2017年 / 296卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Abstract—Let χ (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, χ) from the functional equation of ζ(s). Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments.
引用
收藏
页码：115 / 124
页数：9
相关论文
共 50 条
  • [31] 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
  • [32] SMALL ZEROS OF DIRICHLET L-FUNCTIONS
    WEINBERGER, PJ
    MATHEMATICS OF COMPUTATION, 1975, 29 (129) : 319 - 328
  • [33] DIRICHLET L-FUNCTIONS AND PRIMITIVE CHARACTERS
    APOSTOL, TM
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 31 (02) : 384 - &
  • [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] FORMAL GROUPS AND DIRICHLET L-FUNCTIONS
    KIM, JM
    JOURNAL OF NUMBER THEORY, 1991, 37 (02) : 161 - 167
  • [38] Critical zeros of Dirichlet L-functions
    Conrey, J. Brian
    Iwaniec, Henryk
    Soundararajan, Kannan
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 681 : 175 - 198
  • [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
12345