Special L-values of Drinfeld modules

Abstract

We state and prove a formula for a certain value of the Goss L-function of a Drinfeld module. This gives characteristic-p-valued function field analogues of the class number formula and of the Birch and Swinnerton-Dyer conjecture. The formula and its proof are presented in an entirely self-contained fashion.

to appear in Annals of Mathematics

References in corpus (2)

• A Dirichlet unit theorem for Drinfeld modules
• The Carlitz shtuka

Cited by in corpus (8)

• Arithmetic of positive characteristic L-series values in Tate algebras
• A Herbrand-Ribet theorem for function fields
• Arithmetic of characteristic p special L-values (with an appendix by V. Bosser)
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Log-algebraic identities on Drinfeld modules and special L-values
• An Equivariant Tamagawa Number Formula for Drinfeld Modules and Applications
• Computation of classical and $v$-adic $L$-series of $t$-motives
• On the transcendence of special values of Goss $L$-functions attached to Drinfeld modules