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Texas A&M
Title: Log-algebraicity formulas and special values of Goss L-functions
Abstract: We will consider special values of Goss L-functions for Dirichlet characters at positive integers, which take values in the completion of the rational function field in one variable over a finite field. Building on work of Anderson for the case of L(1,chi), we will deduce various power series identities on tensor powers of the Carlitz module that are "log-algebraic" and in turn use these formulas to access values L(n,chi) for arbitrary n > 0. Moreover, we will relate these L-series values to powers of the Carlitz period and values of Carlitz polylogarithms at algebraic points.