New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner's series

2012/06/02 by Khodabakhsh Hessami Pilehrood, Pilehrood, Khodabakhsh Hessami, Tatiana Hessami Pilehrood +3 · 1 citation
Mathematics · #11A07 #11B39 #11B65 #11B68 #33C45 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1206.0407

openalex publication_date 2012/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences (\1\^a,c,\1\^b), (\2\^a,c,\2\^b) and prove a number of congruences for these sums modulo a prime p. The congruences obtained allow us to find nice p-analogues of Leshchiner's series for zeta values and to refine a result due to M. Hoffman and J. Zhao about the set of generators of the multiple harmonic sums of weight 7 and 9 modulo p. Moreover, we are also able to provide a new proof of Zagier's formula for ζ^*(\2\^a,3,\2\^b) based on a finite identity for partial sums of the zeta-star series.

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