On Dirichlet series with periodic coefficients

被引：11
作者：
Steuding, J [1 ]
机构：
[1] Univ Frankfurt, D-60054 Frankfurt, Germany
来源：
RAMANUJAN JOURNAL | 2002年 / 6卷 / 03期
关键词：
periodic arithmetical functions; Dirichlet series; zero distribution;
D O I：
10.1023/A:1019797315282
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate Dirichlet series L(s, f) = Sigma(n=1)(infinity)f(n)/n(s) with q-periodic coefficients f(n), i.e. f(n+q) = f(n) for all integers n and some fixed integer q, and we prove an asymptotic formula for the number of nontrivial zeros of L(s, f). Further, we give a necessary condition for L(s, f) to have a distribution of the nontrivial zeros symmetrical with respect to the critical line.
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页码：295 / 306
页数：12
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