Modular relation interpretation of the series involving the Riemann zeta values

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.