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OHNO–ZAGIER TYPE RELATIONS FOR MULTIPLE t-VALUES

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

Published online by Cambridge University Press:  11 November 2022

ZHONGHUA LI Open the ORCID record for ZHONGHUA LI[Opens in a new window]  and
YUTONG SONG Open the ORCID record for YUTONG SONG[Opens in a new window]
ZHONGHUA LI*
Affiliation:
School of Mathematical Sciences, Tongji University, No. 1239 Siping Road, Shanghai 200092, PR China
YUTONG SONG
Affiliation:
School of Mathematical Sciences, Tongji University, No. 1239 Siping Road, Shanghai 200092, PR China e-mail: 1853404@tongji.edu.cn
*
e-mail: zhonghua_li@tongji.edu.cn
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Abstract

We study Ohno–Zagier type relations for multiple t-values and multiple t-star values. We represent the generating function of sums of multiple t-(star) values with fixed weight, depth and height in terms of the generalised hypergeometric function $\,_3F_2$ . As applications, we get a formula for the generating function of sums of multiple t-(star) values of maximal height and a weighted sum formula for sums of multiple t-(star) values with fixed weight and depth.

Keywords

multiple t-valuemultiple zeta valuegeneralised hypergeometric function

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 33C20: Generalized hypergeometric series, $_pF_q$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 215 - 226
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by the Fundamental Research Funds for the Central Universities (grant number 22120210552).

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