New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner's series
By Khodabakhsh Hessami Pilehrood, T. H. Pilehrood, Roberto Tauraso. 2012
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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 \zeta^{*}(\{2\}^a,3,\{2\}^b) based on a finite identity for partial sums of the zeta-star series.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/a0675a1cddabd41ded3f4b53feb39ddfae6156af
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In Algebra and Number Theory
In Applied Mathematics
Citations in the corpus
- QUASI-SYMMETRIC FUNCTIONS AND MOD p MULTIPLE HARMONIC SUMS (2004, background): “Tauraso [14], the first few values of cn are the following.”