# Non-Vanishing of L-Functions of Vector-Valued Modular Forms

## TL;DR

This paper proves that for vector-valued modular forms, there are non-zero average L-values and guarantees the existence of at least one form with a non-vanishing L-function, advancing understanding of their analytic properties.

## Contribution

It establishes non-vanishing results for L-functions of vector-valued modular forms and demonstrates the existence of non-vanishing L-functions within a basis.

## Key findings

- Non-vanishing of average L-values for vector-valued modular forms
- Existence of at least one basis element with non-zero L-function
- Conditions under which non-vanishing is guaranteed

## Abstract

We show a non-vanishing result for the averages of L-functions associated with the orthogonal basis of the space of cusp forms of vector-valued modular forms on the full group. We also show the existence of at least one basis element whose L-function does not vanish under certain conditions.