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Weighted sum formula for multiple harmonic sums modulo primes


Authors: Minoru Hirose, Hideki Murahara and Shingo Saito
Journal: Proc. Amer. Math. Soc. 147 (2019), 3357-3366
MSC (2010): Primary 11M32
DOI: https://doi.org/10.1090/proc/14588
Published electronically: April 9, 2019
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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.


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Additional Information

Minoru Hirose
Affiliation: Faculty of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
Email: m-hirose@math.kyushu-u.ac.jp

Hideki Murahara
Affiliation: Nakamura Gakuen University Graduate School, 5-7-1, Befu, Jonan-ku, Fukuoka, 814-0198, Japan
Email: hmurahara@nakamura-u.ac.jp

Shingo Saito
Affiliation: Faculty of Arts and Science, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
Email: ssaito@artsci.kyushu-u.ac.jp

DOI: https://doi.org/10.1090/proc/14588
Keywords: Multiple zeta values, finite multiple zeta values, weighted sum formula, multiple harmonic sums modulo primes
Received by editor(s): August 2, 2018
Received by editor(s) in revised form: December 8, 2018
Published electronically: April 9, 2019
Additional Notes: This work was supported by JSPS KAKENHI Grant, Number JP18J00982, JP18K03243, and JP18K13392.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2019 American Mathematical Society