On identities for zeta values in Tate algebras

Huy Hung Le (1) , Tuan Ngo Dac (2, 3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CNRS - Centre National de la Recherche Scientifique
3 ICJ - Institut Camille Jordan

Zeta values in Tate algebras were introduced by Pellarin in 2012. They are generalizations of Carlitz's 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's zeta values and an explicit formula for Bernoulli-type polynomials attached to Pellarin's zeta values.

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Huy Hung Le, Tuan Ngo Dac. On identities for zeta values in Tate algebras. Transactions of the American Mathematical Society, 2021, 374 (8), pp.5623-5650. ⟨10.1090/tran/8357⟩. ⟨hal-02444867v3⟩