Automata-style proof of Voloch's result on transcendence (Q1914024)

The author gives a new proof of the transcendence of the period of the Tate elliptic curve, a result originally proved by \textit{J. P. Voloch} [J. Number Theory 58, 55-59 (1996; Zbl 0853.11061)]. The author's nice proof is based on a criterium of transcendence due to \textit{G. Christol} [Theor. Comput. Sci. 9, 141-145 (1979; Zbl 0402.68044)], also known as the Christol, Kamae, Mendès-France and Rauzy criterium [\textit{G. Christol}, \textit{T. Kamae}, \textit{M. Mendès-France}, and \textit{G. Rauzy}, Bull. Soc. Math. Fr. 108, 401-419 (1980; Zbl 0472.10035)], which states the equivalence between the algebraicity of a formal power series over a field of positive characteristic and the recognizability of the sequence of its coefficients by a finite automaton. Let us note that this method does not allow one to reach Voloch's result on the transcendence of parameters of algebraic points.