Exact averages of central values of triple product L-functions

TL;DR

This paper derives exact formulas for the average central values of triple product L-functions over certain modular forms, enabling new insights into their non-vanishing properties using a period formula.

Contribution

It provides the first explicit average formulas for triple product L-functions at the central point, extending previous theoretical results with concrete applications.

Findings

Exact formulas for averages of triple product L-values

Applications to non-vanishing of L-values

Utilizes Gross-Kudla period formula

Abstract

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla.