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<p>The <i>t</i>-adic symmetric multiple zeta value is a generalization of the symmetric multiple zeta value from the perspective of the Kaneko–Zagier conjecture. In this paper, we introduce a further generalization with a new parameter <i>s</i>, which we call the (<i>s</i>,&#xa0;<i>t</i>)-adic symmetric multiple zeta value. Then, the (<i>s</i>,&#xa0;<i>t</i>)-adic version of the <i>t</i>-adic double shuffle relations, duality and cyclic sum formula are established. A finite counterpart of the (<i>s</i>,&#xa0;<i>t</i>)-adic symmetric multiple zeta value is also discussed.</p>

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On a lifting of t-adic symmetric multiple zeta values

  • 期刊论文

  • 发表日期：

    2025年6月30日

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  • Minoru Hirose,
  • Hanamichi Kawamura

摘要

The t-adic symmetric multiple zeta value is a generalization of the symmetric multiple zeta value from the perspective of the Kaneko–Zagier conjecture. In this paper, we introduce a further generalization with a new parameter s, which we call the (s, t)-adic symmetric multiple zeta value. Then, the (s, t)-adic version of the t-adic double shuffle relations, duality and cyclic sum formula are established. A finite counterpart of the (s, t)-adic symmetric multiple zeta value is also discussed.