Transcendence of the values of infinite products in several variables. (English) Zbl 1133.11313

Summary: The aim of this paper is to prove the transcendence of certain infinite products. As applications, we obtain necessary and sufficient conditions for transcendence of the value of \[ \prod^\infty_{k=0}(1+a^{(1)}_kz_1^{r^k}+\dots+a^{(m)}_kz_m^{r^k}) \] at appropriate algebraic points, where \(r\geq2\) is an integer and \(\{a^{(i)}_n\}_{n\geq0} (1\leq i\leq m)\) are suitable sequences of algebraic numbers.


11J81 Transcendence (general theory)
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