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

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 ${\mathrm{\Gamma }}_0(N)$ and also provide an equivalent criterion of the grand Riemann hypothesis for the $L$-function associated to the primitive Maass cusp form over ${\mathrm{\Gamma }}_0(N)$.