Corvaja, Pietro; Hančl, Jaroslav A transcendence criterion for infinite products. (English) Zbl 1207.11075 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 18, No. 3, 295-303 (2007). The authors prove a transcendence criterion for certain infinite products of algebraic numbers. For an increasing sequence of positive integers \(a_n\) and an algebraic number \(\alpha>1\), they study the convergent infinite product \(\prod_{n}([\alpha^{a_n}]/\alpha^{a_n})\), where \([\cdot]\) denotes the integral part. It is proved in Theorem 1 that its value is transcendental, under certain hypotheses; whereas Theorem 3 shows that such hypotheses are in a sense unavoidable. This is done by applying a result of the first author and U. Zannier [Acta Math. 193, No. 2, 175–191 (2004; Zbl 1175.11036)]. Reviewer: Olaf Ninnemann (Berlin) Cited in 3 Documents MSC: 11J81 Transcendence (general theory) 11J68 Approximation to algebraic numbers Keywords:transcendence criterion; infinite products Citations:Zbl 1175.11036 PDF BibTeX XML Cite \textit{P. Corvaja} and \textit{J. Hančl}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 18, No. 3, 295--303 (2007; Zbl 1207.11075) Full Text: DOI OpenURL References: [1] P. CORVAJA - U. ZANNIER, Some new applications of the Subspace Theorem . Compos. Math. 131 (2002), 319-340. 303 · Zbl 1010.11038 [2] P. CORVAJA - U. ZANNIER, On the rational approximation to the powers of an algebraic number: Solution of two problems of Mahler and Mend‘es France . Acta Math. 193 (2004), 175-191. · Zbl 1175.11036 [3] W. M. SCHMIDT, Diophantine Approximations and Diophantine Equations . Lecture Notes in Math. 1467, Springer, 1991. · Zbl 0754.11020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.