# The Jensen-P\'{o}lya program for various L-functions

## TL;DR

This paper extends the Jensen-Pólya program to various L-functions, showing that their Jensen polynomials are hyperbolic for all but finitely many cases, providing evidence for the generalized Riemann hypothesis.

## Contribution

It generalizes previous results from the Riemann Xi-function to a broader class of L-functions, supporting the generalized Riemann hypothesis.

## Key findings

- Jensen polynomials for L-functions are hyperbolic except finitely many cases.
- Supports the generalized Riemann hypothesis.
- Extends Pólya's program to new classes of functions.

## Abstract

P\'{o}lya proved in 1927 that the Riemann hypothesis is equivalent to the hyperbolicity of all of the Jensen polynomials of degree $d$ and shift $n$ for the Riemann Xi-function. Recently, Griffin, Ono, Rolen, and Zagier proved that for each degree $d \geq 1$ all of the Jensen polynomials for the Riemann Xi-function are hyperbolic except for possibly finitely many $n$. Here we extend their work by showing the same statement is true for suitable $L$-functions. This offers evidence for the generalized Riemann hypothesis.