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.

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Authors

Lenny Taelman

Mathematical Institute
University of Leiden
P.O. Box 9512
2300 RA Leiden
The Netherlands