# Congruences of alternating multiple harmonic sums

## TL;DR

This paper investigates the congruence properties of alternating multiple harmonic sums, highlighting the roles of Euler numbers and polynomials, extending previous work on non-alternating sums.

## Contribution

It advances the understanding of congruences in alternating multiple harmonic sums, emphasizing the importance of Euler numbers and polynomials.

## Key findings

- Identifies key congruence relations involving Euler numbers
- Establishes new connections between alternating sums and Euler polynomials
- Extends previous results on harmonic sums to the alternating case

## Abstract

In this sequel to arXiv:0905.3327, we continue to study the congruence properties of the alternating version of multiple harmonic sums. As contrast to the study of multiple harmonic sums where Bernoulli numbers and Bernoulli polynomials play the key roles, in the alternating setting the Euler numbers and the Euler polynomials are also essential.