Explicit formulas for Drinfeld modules and their periods

Abstract

We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity.

20 pages

References in corpus (1)

• Algebraic independence of values of Goss L-functions at s=1

Cited by in corpus (9)

• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Log-algebraic identities on Drinfeld modules and special L-values
• Effective rigid analytic trivializations for Drinfeld modules
• Linear equations on Drinfeld modules
• On Furusho's analytic continuation of Drinfeld logarithms
• Special values of Goss $L$-series attached to Drinfeld modules of rank 2
• Identities for Anderson generating functions for Drinfeld modules
• Equidistribution of Gross points over rational function fields
• Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications