# Dale Brownawell

Affiliation: Pennsylvania State University

Email: wdb@math.psu.edu

Title Of Talk: Divided Derivatives of the Carlitz Period

Abstract: Without telling anyone what he was doing, Carlitz defined an analogue of the exponential function and thus of $\pi$ in the function field setting over a finite field. L. Denis showed the algebraic independence of this $\pi$ and its first $p-1$ derivatives. In work begun already with A.J. van der Poorten, we show the algebraic independence of all divided derivatives of this $\pi$. Very recently announced work of M. Papanikolas expresses the fundamental periods of the Anderson-Thakur tensor powers of the Carlitz module in terms of these divided derivatives.