Transcendence of L(1,χs)/Π and automata

Abstract

For the field of formal Laurent series over a finite field, Carlitz defined Π, an analogue of the real number π, and Goss defined analogues of Dirichlet L functions. Damamme proved the transcendence of L(1,χs)/Π using the criteria of de Mathan. In this article we give a proof of the transcendence of L(1,χs)/Π based on the Theorem of Christol and another property of k-automatic sequences.