English

New harmonic number identities with applications

Number Theory 2009-12-15 v1

Abstract

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums k=1nj=1rHk({1}λj)\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j}) when j=1rλj5\sum_{j=1}^r \lambda_j\leq 5. We apply these identities to the study of two congruences modulo a power of a prime.

Keywords

Cite

@article{arxiv.0912.2497,
  title  = {New harmonic number identities with applications},
  author = {Roberto Tauraso},
  journal= {arXiv preprint arXiv:0912.2497},
  year   = {2009}
}
R2 v1 2026-06-21T14:23:14.371Z