A continuous version of multiple zeta functions and multiple zeta values
In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at positive integers (continuous multiple zeta values) satisfy...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.440/ |
| _version_ | 1797651583788384256 |
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| author | Li, Jiangtao |
| author_facet | Li, Jiangtao |
| author_sort | Li, Jiangtao |
| collection | DOAJ |
| description | In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at positive integers (continuous multiple zeta values) satisfy the shuffle product. We give a detailed analysis about the depth structure of continuous multiple zeta values. There are also sum formulas for continuous multiple zeta values. Lastly we calculate some special continuous multiple zeta values in terms of special values of multiple polylogarithms. |
| first_indexed | 2024-03-11T16:16:52Z |
| format | Article |
| id | doaj.art-082c289346774028a1b28597b3838ea1 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:52Z |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-082c289346774028a1b28597b3838ea12023-10-24T14:18:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-03-01361G369771310.5802/crmath.44010.5802/crmath.440A continuous version of multiple zeta functions and multiple zeta valuesLi, Jiangtao0School of Mathematics and Statistics, HNP-LAMA, Central South University, Hunan Province, ChinaIn this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at positive integers (continuous multiple zeta values) satisfy the shuffle product. We give a detailed analysis about the depth structure of continuous multiple zeta values. There are also sum formulas for continuous multiple zeta values. Lastly we calculate some special continuous multiple zeta values in terms of special values of multiple polylogarithms.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.440/ |
| spellingShingle | Li, Jiangtao A continuous version of multiple zeta functions and multiple zeta values Comptes Rendus. Mathématique |
| title | A continuous version of multiple zeta functions and multiple zeta values |
| title_full | A continuous version of multiple zeta functions and multiple zeta values |
| title_fullStr | A continuous version of multiple zeta functions and multiple zeta values |
| title_full_unstemmed | A continuous version of multiple zeta functions and multiple zeta values |
| title_short | A continuous version of multiple zeta functions and multiple zeta values |
| title_sort | continuous version of multiple zeta functions and multiple zeta values |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.440/ |
| work_keys_str_mv | AT lijiangtao acontinuousversionofmultiplezetafunctionsandmultiplezetavalues AT lijiangtao continuousversionofmultiplezetafunctionsandmultiplezetavalues |