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

TL;DR

This paper investigates the average behavior of coefficients associated with triple product L-functions linked to primitive holomorphic cusp forms, providing insights into their statistical properties within number theory.

Contribution

It offers a new analysis of the average behavior of coefficients of triple product L-functions for primitive cusp forms, expanding understanding of their distribution.

Findings

Derived average estimates for coefficients of triple product L-functions

Established connections between coefficients and eigenfunctions of Hecke operators

Enhanced understanding of the statistical properties of these 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 $SL(2,\ \mathbb{Z}).$ Here we call $f(z)$ a primitive cusp form if it is an eighenfunction of all Hecke operators simultaneously.