Arithmetic of positive characteristic L-series values in Tate algebras

Abstract

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules defined over Tate algebras. This enables us to generalize Anderson's log-algebraicity Theorem and Taelman's Herbrand-Ribet Theorem.

final version

References in corpus (1)

• A Herbrand-Ribet theorem for function fields

Cited by in corpus (5)

• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Periods of $t$-modules as special values
• Log-algebraic identities on Drinfeld modules and special L-values
• Special functions and twisted $L$-series
• An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions