We show that Taelman's conjecture on special L-values of Anderson t-modules holds for a large class of t-modules. This class contains all mixed A-finite and uniformizable t-modules whose Hodge-Pink weights are at least 1. As a consequence, we deduce various log-algebraicity identities for tensor powers of the Carlitz module, generalizing the work of Anderson-Thakur.
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. Contents 5. An example: tensor powers of the Carlitz module 13 6. Further reading on related topics 15 References 17
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