Congruences for central binomial sums and finite polylogarithms

TL;DR

This paper establishes congruences modulo prime powers for finite sums involving central binomial coefficients, advancing understanding of their properties in number theory.

Contribution

It introduces new congruences for sums with central binomial coefficients and finite polylogarithms, extending existing mathematical frameworks.

Findings

Proved congruences modulo prime powers for binomial sums

Connected finite sums to polylogarithmic functions

Enhanced understanding of binomial sum properties in modular arithmetic

Abstract

We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomial coefficients $\binom{2k}{k}$.