A bivariate generating function for zeta values and related supercongruences

TL;DR

This paper introduces a new bivariate generating function for zeta values, proves a related combinatorial identity using Wilf-Zeilberger method, and applies it to establish several supercongruences for even zeta values.

Contribution

It presents a novel finite combinatorial identity linked to a bivariate generating function for zeta(2+r+2s) and demonstrates its application to supercongruences.

Findings

Established a new combinatorial identity for zeta values.

Extended Bailey-Borwein-Bradley formula for even zeta values.

Proved several supercongruences using the identity.

Abstract

By using the Wilf-Zeilberger method, we prove a novel finite combinatorial identity related to a bivariate generating function for $\zeta(2+r+2s)$ (an extension of a Bailey-Borwein-Bradley Apery-like formula for even zeta values). Such identity is then applied to show several supercongruences.