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October 2021 Double Dirichlet series associated with arithmetic functions
Kohji Matsumoto, Akihiko Nawashiro, Hirofumi Tsumura
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Kodai Math. J. 44(3): 437-456 (October 2021). DOI: 10.2996/kmj/kmj44303

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

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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

Information

Received: 6 April 2020; Published: October 2021
First available in Project Euclid: 27 October 2021

Digital Object Identifier: 10.2996/kmj/kmj44303

Subjects:
Primary: 11M41
Secondary: 11M06 , 11M26

Keywords: Möbius function , multiple Dirichlet series , Riemann zeta function , von Mangoldt function

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 3 • October 2021
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