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<p>Recently, through the study of <i>q</i>-generalized higher-order Stirling numbers, <i>q</i>-generalized finite multiple zeta functions have been naturally introduced, and their values at roots of unity have been explicitly obtained. When <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10_2025_1235_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\rightarrow 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo stretchy="false">→</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, they are finite multiple zeta functions. In this paper, we obtain some explicit expressions for certain <i>q</i>-multiple <i>t</i>-values at roots of unity. In other words, such expressions are multiple zeta values when the indices of the sum are limited to odd numbers. These finite functions are closely related to Stirling numbers of type B, which have strong relations to the Coxeter group and Artin basis.</p>

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Some explicit values of a q-multiple t-function at roots of unity

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Takao Komatsu,
  • Tianze Wang

摘要

Recently, through the study of q-generalized higher-order Stirling numbers, q-generalized finite multiple zeta functions have been naturally introduced, and their values at roots of unity have been explicitly obtained. When \(q\rightarrow 1\) q → 1 , they are finite multiple zeta functions. In this paper, we obtain some explicit expressions for certain q-multiple t-values at roots of unity. In other words, such expressions are multiple zeta values when the indices of the sum are limited to odd numbers. These finite functions are closely related to Stirling numbers of type B, which have strong relations to the Coxeter group and Artin basis.