EULER–HADAMARD PRODUCTS AND POWER MOMENTS OF SYMMETRIC SQUARE L-FUNCTIONS

Abstract

In this paper we prove asymptotic formulas for general moments of partial Euler products and the first and the second moments of partial Hadamard products related to central values of the family of L-functions associated to the symmetric square lifts of holomorphic modular forms for SL2(ℤ). Then using a hybrid Euler–Hadamard product formula for the central value, we relate these results with conjectures for general power moments of L-functions in this family and with Random Matrix Theory interpretations. This continues the work done previously by Gonek–Hughes–Keating and Bui–Keating for other families of L-functions.