Congruences involving alternating multiple harmonic sum

2009/05/20 by Roberto Tauraso, Tauraso, Roberto · 1 citation
Mathematics · #05A19 (Secondary) #11A07 #11B65 (Primary) 05A10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:05A10 #msc:05A19 #msc:11A07 #msc:11B65

paper · pdf · doi:10.48550/arxiv.0905.3327

openalex publication_date 2009/05/20 · arxiv created 2009/12/24 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any prime prime p\not=2 ∑_k=1^p-1 (-1)^k\over k-1\over 2 \choose k ≡ -∑_k=1^(p-1)/21\over k \pmodp³ by expressing the l.h.s. as a combination of alternating multiple harmonic sums.

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• Congruences of alternating multiple harmonic sums

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