Modular relation interpretation of the series involving the Riemann zeta values

Shigeru Kanemitsu; Hai-Long Li; Haruo Tsukada

doi:10.3792/pjaa.84.154

October 2008 Modular relation interpretation of the series involving the Riemann zeta values

Shigeru Kanemitsu, Hai-Long Li, Haruo Tsukada

Proc. Japan Acad. Ser. A Math. Sci. 84(8): 154-158 (October 2008). DOI: 10.3792/pjaa.84.154

Abstract

We shall locate Katsurada’s results, in our framework of modular relations, on two series involving the values of the Riemann zeta-function, which are decisive generalizations of earleir results of Chowla and Hawkins and of Buschman and Srivastava \textit{et al.} We shall elucidate these results as an improper or a proper modular relation according as the involved parameter $\nu$ exerts effects on the series or not, eventually indicating that they are disguised form of modular relations as given by Theorem 4 in 3.

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Shigeru Kanemitsu, Hai-Long Li, and Haruo Tsukada "Modular relation interpretation of the series involving the Riemann zeta values," Proceedings of the Japan Academy, Series A, Mathematical Sciences 84(8), 154-158, (October 2008). https://doi.org/10.3792/pjaa.84.154

Published: October 2008

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