stimates for automorphic L-functions on the critical line and their applications
Estimates for zeta functions and L-functions on the critical line appear in many applications in number theory. I am especially interested in the automorphic L-functions. The aim of my recently research is to prove a subconvexity bound for the second moment of the Rankin-Selberg L-functions for the Picard group in the spectral aspect. In the case of the modular group, Luo-Sarnak proved the mean Lindeloef hypothesis and improved the error term of the prime geodesic theorem as application. Now I try to improve the estimate by the method of Iwaniec-Michel which gave the proof of the mean Lindeloef hypothesis for the second moment of the symmetric square L-functions in the level aspect.