A transcendence criterion for infinite products
A transcendence criterion for infinite products
We prove a transcendence criterion for certain infinite products of algebraic numbers. Namely, for an increasing sequence of positive integers a_n and an algebraic number \alpha>1 , we consider the convergent infinite product \prod_{n}([\alpha^{a_n}]/\alpha^{a_n}) , where [\cdot] stands for the integral part. We prove (Thm. 1) that its value is …