The Carlitz motive and Carlitz logarithms
by
Matthew Papanikolas
Texas A&M University

The Carlitz exponential function plays many of the roles over global function fields that the usual exponential function does over number fields. For example, its division values provide the basis for an explicit class field theory for F_q(T). Also, it is the uniformizing exponential function for the primary example of a Drinfeld module, the Carlitz module.

In 1997, J. Yu proved the analogue for Carlitz logarithms of A. Baker's celebrated result on linear forms in logarithms. In this talk we will present new results on the algebraic independence of Carlitz logarithms. In particular, by utilizing a Tannakian formalism for Drinfeld modules, we prove that Carlitz logarithms that are linearly independent over F_q(T) are in fact algebraically independent.

Date received: April 30, 2004