Abstract
Multiple zeta values at non-positive integers depend on its limiting process. In this paper, explicit and recurrence formulas to evaluate multiple zeta values at non-positive integers for various limiting processes are given. As applications of them, a classification of multiple zeta values for ordered limits and relationship between multiple zeta values for directional limits and ordered limits are showed. Further, an alternative proof of the conjecture raised by Akiyama, Egami and Tanigawa is also given.
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Acknowledgements
The author would like to express his gratitude to Professor Yasushi Komori for valuable comments. This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
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Sasaki, Y. Evaluation of multiple zeta values for various limiting processes at non-positive integers. Res. number theory 9, 38 (2023). https://doi.org/10.1007/s40993-023-00446-w
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DOI: https://doi.org/10.1007/s40993-023-00446-w