Combinatorial proof of the transcendence of $L(1,χ_s)/Π$

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

No reviews yet.

No comments yet.