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ANALOGUES OF THE AOKI–OHNO AND LE–MURAKAMI RELATIONS FOR FINITE MULTIPLE ZETA VALUES

Part of: Sequences and sets Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  26 December 2018

MASANOBU KANEKO Open the ORCID record for MASANOBU KANEKO [Opens in a new window] ,
KOJIRO OYAMA Open the ORCID record for KOJIRO OYAMA [Opens in a new window]  and
SHINGO SAITO Open the ORCID record for SHINGO SAITO [Opens in a new window]
MASANOBU KANEKO*
Affiliation:
Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan email [email protected]
KOJIRO OYAMA
Affiliation:
1-31-17, Chuo, Aomori-shi, Aomori, 030-0822, Japan email [email protected]
SHINGO SAITO
Affiliation:
Faculty of Arts and Science, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan email [email protected]
*
✉[email protected]
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Abstract

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We establish finite analogues of the identities known as the Aoki–Ohno relation and the Le–Murakami relation in the theory of multiple zeta values. We use an explicit form of a generating series given by Aoki and Ohno.

Keywords

multiple zeta valuefinite multiple zeta valueAoki–Ohno relationLe–Murakami relation

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 11B68: Bernoulli and Euler numbers and polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 34 - 40
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by JSPS KAKENHI Grant Numbers JP16H06336 and JP18K18712.

References

Aoki, T. and Ohno, Y., ‘Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions’, Publ. Res. Inst. Math. Sci. 41 (2005), 329–337.Google Scholar
Hoffman, M., ‘Quasi-symmetric functions and mod p multiple harmonic sums’, Kyushu J. Math. 69 (2015), 345–366.Google Scholar
Kaneko, M., ‘Finite multiple zeta values’, RIMS Kôkyûroku Bessatsu B68 (2017), 175–190 (in Japanese).Google Scholar
Kaneko, M., ‘An introduction to classical and finite multiple zeta values’, Publ. Math. Besançon, to appear.Google Scholar
Kaneko, M. and Zagier, D., Finite multiple zeta values (in preparation).Google Scholar
Le, T. Q. T. and Murakami, J., ‘Kontsevich’s integral for the Homfly polynomial and relation between values of multiple zeta functions’, Topology Appl. 62 (1995), 193–206.Google Scholar
Ohno, Y. and Zagier, D., ‘Multiple zeta values of fixed weight, depth, and height’, Indag. Math. 12 (2001), 483–487.Google Scholar
Sakugawa, K. and Seki, S., ‘On functional equations of finite multiple polylogarithms’, J. Algebra 469 (2017), 323–357.Google Scholar
Yaeo, K., Consideration of Relations among Finite Multiple Zeta Values, Master’s thesis, Tohoku University, 2017 (in Japanese).Google Scholar
Zhao, J., ‘Wolstenholme type theorem for multiple harmonic sums’, Int. J. Number Theory 4(1) (2008), 73–106.Google Scholar
Zhao, J., Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values, Series on Number Theory and Its Applications, 12 (World Scientific, Singapore, 2016).Google Scholar