## 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.

### MSC:

 11J81 Transcendence (general theory)
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### References:

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