New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner’s series
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- by Kh. Hessami Pilehrood, T. Hessami Pilehrood and R. Tauraso PDF
- Trans. Amer. Math. Soc. 366 (2014), 3131-3159 Request permission
Abstract:
In this paper we present some new binomial identities 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 $p$. As a further application we 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.References
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Additional Information
- Kh. Hessami Pilehrood
- Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2
- Email: hessamik@gmail.com
- T. Hessami Pilehrood
- Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2
- Address at time of publication: Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada B3H 3C3
- Email: hessamit@gmail.com
- R. Tauraso
- Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, 00133 Roma, Italy
- Email: tauraso@mat.uniroma2.it
- Received by editor(s): July 11, 2012
- Received by editor(s) in revised form: October 4, 2012
- Published electronically: October 2, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 3131-3159
- MSC (2010): Primary 11A07, 11M32; Secondary 11B65, 11B68
- DOI: https://doi.org/10.1090/S0002-9947-2013-05980-6
- MathSciNet review: 3180742