On identities for zeta values in Tate algebras

Le, Huy Hung; Ngo Dac, Tuan

doi:10.1090/tran/8357

On identities for zeta values in Tate algebras
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by Huy Hung Le and Tuan Ngo Dac PDF

Trans. Amer. Math. Soc. 374 (2021), 5623-5650 Request permission

Abstract:

Zeta values in Tate algebras were introduced by Pellarin in 2012. They are generalizations of Carlitz zeta values and play an increasingly important role in function field arithmetic. In this paper we prove a conjecture of Pellarin on identities for these zeta values. The proof is based on arithmetic properties of Carlitz zeta values and an explicit formula for Bernoulli-type polynomials attached to zeta values in Tate algebras.

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