Transcendental sequences

Jaroslav Hančl

On reciprocal sums of terms of linear recurrences

Jaroslav Hančl, Péter Kiss (1993)

Mathematica Slovaca

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Algebraically unrelated sequences

Jaroslav Hančl (2003)

Mathematica Slovaca

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A note to the transcendence of special infinite series

Jaroslav Hančl, Pavel Rucki (2006)

Mathematica Slovaca

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A note on the transcendence of infinite products

Jaroslav Hančl, Ondřej Kolouch, Simona Pulcerová, Jan Štěpnička (2012)

Czechoslovak Mathematical Journal

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The paper deals with several criteria for the transcendence of infinite products of the form $\prod_{n = 1}^{\infty} [b_{n} α^{a_{n}}] / b_{n} α^{a_{n}}$ where $α > 1$ is a positive algebraic number having a conjugate $α^{*}$ such that $α \neq | α^{*} | > 1$ , ${a_{n}}_{n = 1}^{\infty}$ and ${b_{n}}_{n = 1}^{\infty}$ 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...

Displaying similar documents to “Transcendental sequences”

On reciprocal sums of terms of linear recurrences

Algebraically unrelated sequences

A note to the transcendence of special infinite series

A note on the transcendence of infinite products