On identities for zeta values in Tate algebras

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 talk, we will present some related conjectures proposed by Pellarin. Then, we will study the Bernoulli-type polynomials attached to these zeta values. By a combinatorial method, we can also provide 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.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper | slides )

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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