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Weighted sum formula for multiple harmonic sums modulo primes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Apr 2019Embargo end date: 01 Jan 2018 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 147, pages 3,357-3,366 (issn: 0002-9939, eissn: 1088-6826, Copyright policy )
Authors: Hirose, Minoru; Murahara, Hideki; Saito, Shingo;

doi: 10.1090/proc/14588 , 10.48550/arxiv.1808.00844

arXiv: 1808.00844

Weighted sum formula for multiple harmonic sums modulo primes

Abstract

In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple harmonic sums. We also conjecture several weighted sum formulas of similar flavor for finite multiple zeta values.

Related Organizations
Keywords

Mathematics - Number Theory, weighted sum formula, Multiple Dirichlet series and zeta functions and multizeta values, FOS: Mathematics, Number Theory (math.NT), multiple zeta values, 11M32, finite multiple zeta values, multiple harmonic sums modulo primes

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
hybrid