We prove a transcendence criterion for certain infinite products of algebraic numbers. Namely, for an increasing sequence of positive integers and an algebraic number , we consider the convergent infinite product , where stands for the integral part. We prove (Thm. 1) that its value is transcendental, under certain hypothesis; Thm. 3 will show that such hypothesis are in a sense unavoidable.
Cite this article
Pietro Corvaja, Jaroslav Hancl, A transcendence criterion for infinite products. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 295–303DOI 10.4171/RLM/496