NATURAL BOUNDARIES OF A FAMILY OF DIRICHLET SERIES

作者：Zaharescu Alexandru^*; Zaki Mohammad

来源：Rocky Mountain Journal of Mathematics, 2013, 43(2): 661-676.

DOI：10.1216/RMJ-2013-43-2-661

• Zeta and L-functions
• Dirichlet series
• analytic continuation

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.

• 出版日期2013