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ON A WEIGHTED SUM OF MULTIPLE $\mathbf{{T}}$-VALUES OF FIXED WEIGHT AND DEPTH

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  19 March 2021

YOSHIHIRO TAKEYAMA Open the ORCID record for YOSHIHIRO TAKEYAMA [Opens in a new window]
YOSHIHIRO TAKEYAMA*
Affiliation:
Department of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
*
e-mail: takeyama@math.tsukuba.ac.jp
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Abstract

The multiple T-value, which is a variant of the multiple zeta value of level two, was introduced by Kaneko and Tsumura [‘Zeta functions connecting multiple zeta values and poly-Bernoulli numbers’, in: Various Aspects of Multiple Zeta Functions, Advanced Studies in Pure Mathematics, 84 (Mathematical Society of Japan, Tokyo, 2020), 181–204]. We show that the generating function of a weighted sum of multiple T-values of fixed weight and depth is given in terms of the multiple T-values of depth one by solving a differential equation of Heun type.

Keywords

Heun’s equationhypergeometric functionmultiple T-value

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 33C90: Applications
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 398 - 405
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was partially supported by JSPS KAKENHI grant number 18K03233.

References

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