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We give a combinatorial proof of the transcendence of $L(1,\chi_s)/\Pi$,where $L(1,\chi_s)$ (resp. $\Pi$) is the analogue in characteristic $p$ of thefunction $L$ of Dirichlet (resp. $\pi$). This result has been proven by G.Damamme using the criteria of de Mathan. Our proof is based on the Theorem ofChristol and another property of $k$-automatic sequences.

Combinatorial proof of the transcendence of $L(1,\chi_s)/\Pi$