The Riemann Zeta Function on Arithmetic Progressions

被引：8

作者：

Steuding, Joern ^{[1
]}

Wegert, Elias ^{[2
]}

机构：

[1] Univ Wurzburg, Dept Math, D-97218 Wurzburg, Germany

[2] TU Bergakad Freiberg, Inst Appl Anal, D-09596 Freiberg, Germany

来源：

EXPERIMENTAL MATHEMATICS | 2012年 / 21卷 / 03期

关键词：

Riemann zeta function; value distribution; arithmetic progression;

D O I：

10.1080/10586458.2012.651410

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove asymptotic formulas for the first discrete moment of the Riemann zeta function on certain vertical arithmetic progressions inside the critical strip. The results give some heuristic arguments for a stochastic periodicity that we observed in the phase portrait of the zeta function.

引用

页码：235 / 240

页数：6

共 8 条

[1]

Borwein P., 2007, The Riemann hypothesis: a resource for the afficionado and virtuoso alike

[2]

GOOD A, 1978, J REINE ANGEW MATH, V303, P51

[3]

Ivie A., 1985, RIEMANN ZETA FUNCTIO

[4]

Putnam CR., 1954, AM J MATH, V76, P828, DOI [10.2307/2372656, DOI 10.2307/2372656]

[5]

Putnam CR., 1954, Am. J. Math, V76, P97, DOI [10.2307/2372402, DOI 10.2307/2372402]

[6] Arithmetic progressions of zeros of the Riemann zeta function [J].

van Frankenhuijsen, M .

JOURNAL OF NUMBER THEORY, 2005, 115 (02) :360-370

[7]

Wegert E., 2011, Notices Amer. Math. Soc., V58, P768

[8]

Wegert E, 2010, COMPUT METH FUNCT TH, V10, P639

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