On an extension of a theorem of Tunnell
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.
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 .