A transcendence criterion for infinite products

  • Pietro Corvaja

    Università di Udine, Italy
  • Jaroslav Hancl

    University of Ostrava, Czech Republic


We prove a transcendence criterion for certain infinite products of algebraic numbers. Namely, for an increasing sequence of positive integers ana_n and an algebraic number α>1\alpha>1, we consider the convergent infinite product n([αan]/αan)\prod_{n}([\alpha^{a_n}]/\alpha^{a_n}), where [][\cdot] 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