A sum-shuffle formula for zeta values in Tate algebras
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1025-1048.

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.

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.

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DOI : https://doi.org/10.5802/jtnb.1010
Classification : 11M38
Mots clés : Multiple zeta values, Function field arithmetic, Carlitz zeta values
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     title = {A sum-shuffle formula for zeta values in {Tate} algebras},
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Federico Pellarin. A sum-shuffle formula for zeta values in Tate algebras. Journal de Théorie des Nombres de Bordeaux, Tome 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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