On special values at integers of $L$-functions of Jacobi theta products of weight 3

Abstract

In this paper, we consider $L$-functions of modular forms of weight 3, which are products of the Jacobi theta series, and express their special values at $s=3$, $4$ in terms of special values of Kamp\'e de F\'eriet hypergeometric functions. Moreover, via $L$-values, we give some relations between special values of Kamp\'e de F\'eriet hypergeometric functions and generalized hypergeometric functions.