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On the linear relations among parametrized multiple series

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Abstract

Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these parametrized multiple series. Specifically, we prove the following two statements: the linear part of the Kawashima relation for multiple zeta values can be generalized to parametrized multiple series; any linear relations among the parametrized multiple series can be written as a linear combination of the linear part of the Kawashima relation.

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Authors and Affiliations

  1. Institute for Advanced Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan

    Minoru Hirose

  2. The University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami-ku, Kitakyushu, Fukuoka, 802-8577, Japan

    Hideki Murahara

  3. Institute of Mathematics for Industry, 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 Hideki Murahara.

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This work was supported by JSPS KAKENHI Grant Numbers JP18K13392 and JP19K14511.

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Hirose, M., Murahara, H. & Onozuka, T. On the linear relations among parametrized multiple series. Ramanujan J 60, 1095–1105 (2023). https://doi.org/10.1007/s11139-022-00658-1

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  • DOI: https://doi.org/10.1007/s11139-022-00658-1

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