New harmonic number identities with applications

2009/12/13 by Roberto Tauraso, Tauraso, Roberto
Mathematics · Physics and Astronomy · #05A10 #05A19 #11A07 #11B65 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0912.2497

openalex publication_date 2009/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ∑_k=1ⁿ ∏_j=1^r H_k(\1\^λ_j) when ∑_j=1^r λ_j≤ 5. We apply these identities to the study of two congruences modulo a power of a prime.

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