A sum-shuffle formula for zeta values in Tate algebras

Federico Pellarin

doi:10.5802/jtnb.1010

Federico Pellarin ¹

¹ Institut Camille Jordan UMR 5208 Site de Saint-Etienne 23 rue du Dr. P. Michelon 42023 Saint-Etienne, France

Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 1025-1048.

Abstract
Résumé

We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in [9]. This follows from an analog result for double twisted power sums, implying that an $𝔽_{p}$ -vector space generated by multiple zeta values in Tate algebras is an $𝔽_{p}$ -algebra.

Nous démontrons une formule de mélange pour des valeurs zêta multiples dans des algèbres de Tate (en caractéristique non nulle) introduites dans [9]. Ce résultat se déduit d’un résultat analogue pour les sommes de puissances tordues et implique que le $𝔽_{p}$ -espace vectoriel des valeurs zêta multiples dans les algèbres de Tate est une $𝔽_{p}$ -algèbre.

Received: 2016-10-05
Revised: 2017-02-10
Accepted: 2017-03-02
Published online: 2017-12-12

DOI: 10.5802/jtnb.1010

Classification: 11M38
Keywords: Multiple zeta values, Function field arithmetic, Carlitz zeta values

Author's affiliations:

Federico Pellarin ¹

¹ Institut Camille Jordan UMR 5208 Site de Saint-Etienne 23 rue du Dr. P. Michelon 42023 Saint-Etienne, France

License:

CC-BY-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Federico Pellarin. A sum-shuffle formula for zeta values in Tate algebras. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 1025-1048. doi : 10.5802/jtnb.1010. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1010/

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Cited by

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[2] Bruno Anglès; Federico Pellarin Functional identities for $L$ -series values in positive characteristic, J. Number Theory, Volume 142 (2014), pp. 223-251 | DOI | Zbl

[3] Bruno Anglès; Federico Pellarin Universal Gauss-Thakur sums and $L$ -series, Invent. Math., Volume 200 (2015) no. 2, pp. 653-669 | DOI | Zbl

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[10] Federico Pellarin; Rudolph Perkins On twisted $A$ -harmonic sums and Carlitz finite zeta values (2016) (https://arxiv.org/abs/1512.05953)

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