# Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

## TL;DR

This paper establishes new identities for Bernoulli polynomials, linking them to multiple Tornheim zeta functions, and reveals their structure as products of linear factors, with implications for number theory.

## Contribution

It introduces a sequence of nonlinear Bernoulli polynomial identities connected to multiple Tornheim zeta functions, utilizing Eulerian and higher-order Bernoulli polynomial properties.

## Key findings

- Each Bernoulli polynomial expression is a multiple of a product of linear factors.
- Special Bernoulli number cases relate to multiple Tornheim zeta functions.
- The proof leverages properties of Eulerian and higher-order Bernoulli polynomials.

## Abstract

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product of linear factors. The special case of Bernoulli numbers has important applications in the study of multiple Tornheim zeta functions. The proof of the main result relies on properties of Eulerian polynomials and higher-order Bernoulli polynomials.