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ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES

Part of: Combinatorics Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  24 July 2019

HIDEKI MURAHARA Open the ORCID record for HIDEKI MURAHARA [Opens in a new window]  and
TAKUYA MURAKAMI Open the ORCID record for TAKUYA MURAKAMI [Opens in a new window]
HIDEKI MURAHARA*
Affiliation:
Nakamura Gakuen University, 5-7-1 Befu Jonan-ku Fukuoka-shi, Fukuoka, 814-0198, Japan email [email protected]
TAKUYA MURAKAMI
Affiliation:
Graduate School of Mathematics, Kyushu University, 744 Motooka Fukuoka-shi Fukuoka, 819-0395, Japan email [email protected]
*
✉[email protected]
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Abstract

We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

Keywords

multiple zeta valuesfinite multiple zeta valuesOhno’s relationOhno-type relationderivation relation

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 05A19: Combinatorial identities, bijective combinatorics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 23 - 34
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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References

Eie, M., Liaw, W.-C. and Ong, Y. L., ‘A restricted sum formula among multiple zeta values’, J. Number Theory 129 (2009), 908–921.Google Scholar
Horikawa, Y., Oyama, K. and Murahara, H., ‘A note on derivation relations for multiple zeta values and finite multiple zeta values’, Preprint, 2018, arXiv:1809.08389[NT].Google Scholar
Ihara, K., Kaneko, M. and Zagier, D., ‘Derivation and double shuffle relations for multiple zeta values’, Compos. Math. 142 (2006), 307–338.Google Scholar
Kaneko, M., ‘Finite multiple zeta values’, RIMS Kôkyûroku Bessatsu B68 (2017), 175–190 (in Japanese).Google Scholar
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Kaneko, M. and Zagier, D., ‘Finite multiple zeta values’, in preparation.Google Scholar
Murahara, H., ‘Derivation relations for finite multiple zeta values’, Int. J. Number 13 (2017), 419–427.Google Scholar
Oyama, K., ‘Ohno-type relation for finite multiple zeta values’, Kyushu J. Math. 72 (2018), 277–285.Google Scholar
Tanaka, T., ‘Restricted sum formula and derivation relation for multiple zeta values’, Preprint, 2013, arXiv:1303.0398 [NT].Google Scholar