Recent Developments in the Theory of Anderson Modules

Let K be a global function field over a finite field of characteristic p and let A be the ring of elements of K which are regular outside a fixed place of K. This report presents recent developments in the arithmetic of special L-values of Anderson A-modules. Provided that p does not divide the class number of K, we prove an “analytic class number formula” for Anderson A-modules with the help of a recent work of Debry. For tensor powers of the Carlitz module, we explain how to derive several log-algebraicity results from the class number formula for these Anderson modules.