Weighted sum formula for multiple harmonic sums modulo primes
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- by Minoru Hirose, Hideki Murahara and Shingo Saito PDF
- Proc. Amer. Math. Soc. 147 (2019), 3357-3366 Request permission
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.References
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Additional Information
- Minoru Hirose
- Affiliation: Faculty of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
- MR Author ID: 924685
- 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
- MR Author ID: 1169647
- Email: hmurahara@nakamura-u.ac.jp
- Shingo Saito
- Affiliation: Faculty of Arts and Science, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
- MR Author ID: 783465
- Email: ssaito@artsci.kyushu-u.ac.jp
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3357-3366
- MSC (2010): Primary 11M32
- DOI: https://doi.org/10.1090/proc/14588
- MathSciNet review: 3981114