On the average behavior of coefficients related to triple product $L$-functions

Abstract

In this paper, we study the average behaviour of the coefficients of triple product L-functions and some related L-functions corresponding to normalized primitive holomorphic cusp form f ( z ) of weight k for the full modular group SL (2 , Z ) . Here we call f ( z ) a primitive cusp form if it is an eighenfunction of all Hecke operators simultane-ously.