A transcendence criterion for infinite products
Pietro Corvaja
Università di Udine, ItalyJaroslav Hancl
University of Ostrava, Czech Republic
![A transcendence criterion for infinite products cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-18-issue-3.png&w=3840&q=90)
Abstract
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. 295–303
DOI 10.4171/RLM/496