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A note on the transcendence of infinite products

Jaroslav Hančl;  Ondřej Kolouch;  Simona Pulcerová;  Jan Štěpnička — 2012

Czechoslovak Mathematical Journal

The paper deals with several criteria for the transcendence of infinite products of the form ∏ n = 1 ∞ [ b n α a n ] / b n α a n where α > 1 is a positive algebraic number having a conjugate α * such that α ≠ | α * | > 1 , { a n } n = 1 ∞ and { b n } n = 1 ∞ are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès France, Acta...

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