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$t$-adic symmetric multiple zeta values for indices in which 1 and 3 appear alternately

Minoru Hirose, Hideki Murahara, Shingo Saito Acta Arithmetica MSC: Primary 11M32; Secondary 05A19 DOI: 10.4064/aa231109-9-7 Published online: 10 October 2024

Abstract

This paper deals with the $t$-adic symmetric multiple zeta values modulo $t^m$ without modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values that can be expressed as a polynomial of the Riemann zeta values, and give a conjecturally complete list of explicit formulas for such values.

Authors

  • Minoru HiroseGraduate School of Science and Engineering
    Kagoshima University
    Kagoshima, 890-0065, Japan
    e-mail
  • Hideki MuraharaThe University of Kitakyushu
    Kitakyushu, Fukuoka, 802-8577, Japan
    e-mail
  • Shingo SaitoFaculty of Arts and Science
    Kyushu University
    Fukuoka, 819-0395, Japan
    e-mail

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