Higher power moments of symmetric square L-function

Abstract

Let f(z) be a Maass cusp form for the full modular group SL2(Z). And let λsym2f(n) be the n-th coefficient of symmetric square L-function associated with f(z). For A≥2 fixed we define M(A) as the infimum of all numbers M such that∫1T|L(1/2+it,sym2f)|Adt≪fTM+ϵ, where L(s,sym2f) is the automorphic L-function attached to f. In this paper, we will establish the upper bounds of M(A) and get the zero density estimates for L(s,sym2f).