Equivalent criterion for the grand Riemann hypothesis associated with Maass cusp forms

Abstract

In this article, we obtain transformation formulas analogous to the identity of Ramanujan, Hardy and Littlewood in the setting of primitive Maass cusp form over the congruence subgroup $\Gamma _0(N)$ and also provide an equivalent criterion of the grand Riemann hypothesis for the $L$ -function associated with the primitive Maass cusp form over $\Gamma _0(N)$ .