An introduction to classical and finite multiple zeta values

Kaneko, Masanobu

Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 103-129.

Nous décrivons certaines propriétés basiques des valeurs de fonctions zétas multiples. Nous explicitons en particulier la théorie des régularisations et son lien avec une identité, obtenue en collaboration avec S. Yamamoto, entre certaines intégrales et séries. Nous présentons également les deux versions « finies » des valeurs zétas multiples et un lien conjectural entre elles découvert conjointement avec D. Zagier.

We review some basic properties of multiple zeta values, in particular the theory of regularization and its connection to an identity between certain integral and series discovered in collaboration with S. Yamamoto. We also introduce the two “finite” versions of multiple zeta values, and a conjectural connection between them, which were discovered jointly with D. Zagier.

Classification : 11M32, 11B68
Mots clés : multiple zeta values, regularization, finite multiple zeta values

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