Residue Theorem, Regularization and Parity Theorem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908753985536000 |
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| author | Li, Jia Xu, Ce |
| author_facet | Li, Jia Xu, Ce |
| contents | In this paper, we employ contour integration and residue calculus to derive explicit parity formulas for (cyclotomic) multiple zeta values (MZVs). A key innovation lies in applying double shuffle regularization to the contour integrals, which leads to two distinct regularized parity formulas-one via shuffle and one via stuffle regularization. Notably, this demonstrates for the first time that the contour integral method can be extended to the regularized setting (including the case $k_r=1$), thereby overcoming a limitation of previous approaches. Our results not only provide explicit parity relations at arbitrary depths but also lay the groundwork for extending this technique to other variants of multiple zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Residue Theorem, Regularization and Parity Theorem Li, Jia Xu, Ce Number Theory 11M32, 11M99 In this paper, we employ contour integration and residue calculus to derive explicit parity formulas for (cyclotomic) multiple zeta values (MZVs). A key innovation lies in applying double shuffle regularization to the contour integrals, which leads to two distinct regularized parity formulas-one via shuffle and one via stuffle regularization. Notably, this demonstrates for the first time that the contour integral method can be extended to the regularized setting (including the case $k_r=1$), thereby overcoming a limitation of previous approaches. Our results not only provide explicit parity relations at arbitrary depths but also lay the groundwork for extending this technique to other variants of multiple zeta values. |
| title | Residue Theorem, Regularization and Parity Theorem |
| topic | Number Theory 11M32, 11M99 |
| url | https://arxiv.org/abs/2601.05024 |