Log-algebraic identities on Drinfeld modules and special L-values

Abstract

We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special values of Goss L-functions are linear forms in Drinfeld logarithms and are transcendental.

21 pages

References in corpus (1)

• Equivariant special L-values of abelian t-modules

Cited by in corpus (4)

• An Equivariant Tamagawa Number Formula for Drinfeld Modules and Applications
• Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients
• Special values of Goss $L$-series attached to Drinfeld modules of rank 2
• On the transcendence of special values of Goss $L$-functions attached to Drinfeld modules