Zeros of the Lerch Transcendent Function

被引：1

作者：

Garunkstis, Ramunas ^{[1
]}

Grigutis, Andrius ^{[1
]}

机构：

[1] Vilnius Univ, LT-03225 Vilnius, Lithuania

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2012年 / 17卷 / 02期

关键词：

polylogarithm; Lerch transcendent; zero distribution;

D O I：

10.3846/13926292.2012.662532

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the distribution of zeros of the Lerch transcendent function Phi(q, s, alpha) = Sigma(infinity)(n=0) q(n) (n + alpha)(-s). We find an upper and lower estimates of zeros of the function Phi(q, s, alpha) in any rectangle {s : sigma(1) < Re s < sigma(2) <= 1.73 ... , 0 < Im s <= T}. Further we are interested in a computer calculations concerning the zeros of Phi(q, s, alpha) in {s : Re s > 1, 0 < Im s <= 1000}.

引用

页码：245 / 250

页数：6

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