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Recent Developments in the Theory of Anderson Modules
Bruno Anglès
,
Tuan Ngo Dac
,
Floric Tavares Ribeiro
Abstract
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.