# Bagchi's Theorem for families of automorphic forms

## TL;DR

This paper extends Bagchi's and Voronin's universality theorems to families of primitive cusp forms of weight 2 and prime level, exploring conditions for broader applicability to automorphic L-functions.

## Contribution

It proves versions of Bagchi's and Voronin's theorems for specific automorphic form families and discusses potential generalizations.

## Key findings

- Established universality results for cusp form families
- Identified conditions for applying the theorems to broader automorphic L-functions
- Enhanced understanding of the distribution of automorphic L-functions

## Abstract

We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L$-functions.