Abstract
We prove that any multiple t-value of maximal height (that is, all components of the index are greater than 1) can be written as a rational linear combination of multiple zeta values by using Glanois’s theorem. We also prove that each multiple zeta value is a \({\mathbb {Q}}\)-linear combination of multiple t-values where all components of the index are 2 or 3. Further, we prove some results on multiple T-values, as conjectured by Kaneko–Tsumura.
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Acknowledgements
The author would like to thank Professor Masanobu Kaneko for valuable comments and suggestions. The author would also like to thank the anonymous referee for many helpful comments.
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Communicated by Wei Zhang.
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This work was supported in part by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University, and the JSPS KAKENHI Grant Number JP16H06336.
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Murakami, T. On Hoffman’s t-values of maximal height and generators of multiple zeta values. Math. Ann. 382, 421–458 (2022). https://doi.org/10.1007/s00208-021-02209-3
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DOI: https://doi.org/10.1007/s00208-021-02209-3