On ...-Adic Representations Attached to Modular Forms.
We consider to be the -function attached to a particular automorphic form on . We establish an upper bound for the mean square estimate on the critical line of Rankin-Selberg -function . As an application of this result, we give an asymptotic formula for the discrete sum of coefficients of .
We prove the optimal upper bound where runs over an orthonormal basis of Maass cusp forms of prime level and bounded spectral parameter.