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
收藏
页码：661 / 676
页数：16
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