Double Dirichlet series associated with arithmetic functions

2018/01/13 by Matsumoto, Kohji, Nawashiro, Akihiko, Tsumura, Hirofumi
#11M06 #11M26 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.04444

Abstract

We consider double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the Möbius function, and so on. We show analytic continuations of them by use of the Mellin-Barnes integral. Furthermore we observe their reverse values at non-positive integer points.

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