Hypertranscendence and algebraic independence of certain infinite products
Hypertranscendence and algebraic independence of certain infinite products
We study infinite products $F(z)=\prod_{j\ge0}p(z^{d^j})$, where $d\ge2$ is an integer and $p\in\mathbb{C}[z]$ with $p(0)=1$ has at least one zero not lying on the unit circle. In that case, $F$ is a transcendental function and we are mainly interested in