Geodesic
Théorie des nombres
A continuous version of multiple zeta functions and multiple zeta values
Li, Jiangtao1
1 School of Mathematics and Statistics, HNP-LAMA, Central South University, Hunan Province, China
Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 697-713

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In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on 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.

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DOI : 10.5802/crmath.440
Classification : 11M32

Li, Jiangtao 1

1 School of Mathematics and Statistics, HNP-LAMA, Central South University, Hunan Province, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A continuous version of multiple zeta functions and multiple zeta values},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {697--713},
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Li, Jiangtao. A continuous version of multiple zeta functions and multiple zeta values. Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 697-713. doi: 10.5802/crmath.440

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