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\({\mathbb {Q}}\)-linear relations of specific families of multiple zeta values and the linear part of Kawashima’s relation

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Abstract

In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima’s relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As a corollary of our main results, we also see that the duality formula and the derivation relation are deduced from the linear part of Kawashima’s relation.

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Acknowledgements

The authors would like to thank Professor Masanobu Kaneko for valuable comments. This work was supported by JSPS KAKENHI Grant Numbers JP18J00982, JP18K13392.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Minoru Hirose

  2. Nakamura Gakuen University Graduate School, 5-7-1, Befu, Jonan-ku, Fukuoka, 814-0198, Japan

    Hideki Murahara

  3. Multiple Zeta Research Center, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Tomokazu Onozuka

Authors
  1. Minoru Hirose
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  2. Hideki Murahara
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  3. Tomokazu Onozuka
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Correspondence to Tomokazu Onozuka.

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Hirose, M., Murahara, H. & Onozuka, T. \({\mathbb {Q}}\)-linear relations of specific families of multiple zeta values and the linear part of Kawashima’s relation. manuscripta math. 164, 455–465 (2021). https://doi.org/10.1007/s00229-020-01191-5

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  • DOI: https://doi.org/10.1007/s00229-020-01191-5

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