Some Results On Maass Forms

In this paper, we prove several results on Maass forms. Firstly, via Kutznetsov trace for-mula, we reprove a theorem which states that there exist infinitely many linearly independent even Maass forms. Secondly we show the non-singularity of a class of automorphic L-functions at zero by Voronoi formula. Thirdly we utilize a technique due to M. Vigneras to verify the Selberg Eigenvalue Conjecture over some special arithmetic subgroups. Then we prove the up-permost result of this paper:a criteria to verify the equality of two Maass forms based on some common property of the related Rankin-Selberg L-functions. Finally we give an equivalent condition which guarantees the dimension of the sum of Maass form over Heegner points or cycles to be 1.