Weighted sum formula for multiple harmonic sums modulo primes

Minoru Hirose; Hideki Murahara; Shingo Saito

doi:10.1090/proc/14588

Weighted sum formula for multiple harmonic sums modulo primes

Minoru Hirose, Hideki Murahara, Shingo Saito

Division for Theoretical Natural Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	3357-3366
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	8
DOIs	https://doi.org/10.1090/proc/14588
Publication status	Published - 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/14588

Cite this

@article{7d7a8250461e41b596b3d39abb0ab391,

title = "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.",

author = "Minoru Hirose and Hideki Murahara and Shingo Saito",

note = "Funding Information: Received by the editors August 2, 2018, and, in revised form, December 8, 2018. 2010 Mathematics Subject Classification. Primary 11M32. Key words and phrases. Multiple zeta values, finite multiple zeta values, weighted sum formula, multiple harmonic sums modulo primes. This work was supported by JSPS KAKENHI Grant, Number JP18J00982, JP18K03243, and JP18K13392. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

doi = "10.1090/proc/14588",

language = "English",

volume = "147",

pages = "3357--3366",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "8",

}

TY - JOUR

T1 - Weighted sum formula for multiple harmonic sums modulo primes

AU - Hirose, Minoru

AU - Murahara, Hideki

AU - Saito, Shingo

N1 - Funding Information: Received by the editors August 2, 2018, and, in revised form, December 8, 2018. 2010 Mathematics Subject Classification. Primary 11M32. Key words and phrases. Multiple zeta values, finite multiple zeta values, weighted sum formula, multiple harmonic sums modulo primes. This work was supported by JSPS KAKENHI Grant, Number JP18J00982, JP18K03243, and JP18K13392. Publisher Copyright: © 2019 American Mathematical Society.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074208094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074208094&partnerID=8YFLogxK

U2 - 10.1090/proc/14588

DO - 10.1090/proc/14588

M3 - Article

AN - SCOPUS:85074208094

SN - 0002-9939

VL - 147

SP - 3357

EP - 3366

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Weighted sum formula for multiple harmonic sums modulo primes

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this