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, and determine the location of singularities. Furthermore we observe their "reverse" values at non-positive integer points.
Funding Statement
This work was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research No. 25287002 (K. Matsumoto) and No. 15K04788 (H. Tsumura).
Acknowledgment
The authors are sincerely grateful to Professors Hirotaka Akatsuka, Hideaki Ishikawa and Masatoshi Suzuki for their useful advice.
Citation
Kohji Matsumoto. Akihiko Nawashiro. Hirofumi Tsumura. "Double Dirichlet series associated with arithmetic functions." Kodai Math. J. 44 (3) 437 - 456, October 2021. https://doi.org/10.2996/kmj/kmj44303
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