NATURAL BOUNDARIES OF A FAMILY OF DIRICHLET SERIES

被引：1

作者：

Zaharescu, Alexandru ^{[1
,2
]}

Zaki, Mohammad ^{[3
]}

机构：

[1] Acad Romana, Inst Math, Bucharest 014700, Romania

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Ohio No Univ, Dept Math, Ada, OH 45810 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2013年 / 43卷 / 02期

关键词：

Zeta and L-functions; Dirichlet series; analytic continuation; EULER PRODUCTS;

D O I：

10.1216/RMJ-2013-43-2-661

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the natural boundary of the Dirichlet series F-q,F-b,F-H,F-alpha (s) - Sigma(m,k >= 1 mk b (mod q)) II(alpha log(m + k))Lambda(m)Lambda(k)/(m + k)(s), where. is the classical Von Mangoldt function, H is a smooth periodic function with period 1, alpha > 0 is a real number and b, q > 0 are integers with (b, q) = 1.

引用

页码：661 / 676

页数：16

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