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 $SL(2,\mathbbZ).$ Here we call $f(z)$ a primitive cusp form if it is an eigenfunction of all Hecke operators simultaneously.