On identities for zeta values in Tate algebras

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 talk, we will present some related conjectures proposed by Pellarin. Then, we will study the Bernoulli-type polynomials attached to these zeta values. By combinatorial method, we can formulate some explicit formulas. We will demonstrate how to use these results to prove a conjecture of Pellarin on identities for zeta values in Tate algebras.