Abstract
This paper is a continuation of our previous work on double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the Möbius function, and so on. We consider the analytic behaviour around the non-positive integer points on singularity sets which are points of indeterminacy. In particular, we show a certain reciprocity law of their residues. Also on this occasion we correct some inaccuracies in our previous paper.
Funding Statement
This work was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research No. 22K03267 (K. Matsumoto) and No. 21K03168 (H. Tsumura).
Acknowledgment
The authors are sincerely grateful to Professor Masatoshi Suzuki who first pointed out a mistake in [10]. The authors also thank the referee for valuable suggestions and comments.
Citation
Kohji Matsumoto. Hirofumi Tsumura. "Double Dirichlet series associated with arithmetic functions II." Kodai Math. J. 46 (1) 10 - 30, March 2023. https://doi.org/10.2996/kmj46102
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