About: A note on the transcendence of infinite products

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The paper deals with several criteria for the transcendence of infinite products of the form $\prod_{n=1}^{\infty}{[b_n \alpha^{a_n}]/ b_n \alpha^{a_n}}$ where $\alpha > 1$ is a positive algebraic number having a conjugate $\alpha^$ such that $\alpha \not= \|\alpha^\| > 1$, $\{a_n\}_{n=1}^{\infty}$ 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 Mend`es France, Acta Math. 193, (2004), 175–191). The paper deals with several criteria for the transcendence of infinite products of the form $\prod_{n=1}^{\infty}{[b_n \alpha^{a_n}]/ b_n \alpha^{a_n}}$ where $\alpha > 1$ is a positive algebraic number having a conjugate $\alpha^$ such that $\alpha \not= \|\alpha^\| > 1$, $\{a_n\}_{n=1}^{\infty}$ 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 Mend`es France, Acta Math. 193, (2004), 175–191). (en)
Title	A note on the transcendence of infinite products A note on the transcendence of infinite products (en)
skos:prefLabel	A note on the transcendence of infinite products A note on the transcendence of infinite products (en)
skos:notation	RIV/61989100:27510/12:86084248!RIV13-MSM-27510___
http://linked.open...avai/predkladatel	Ekonomická fakulta
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0070), P(GAP201/12/2351), P(ME09017), S, Z(MSM6198898701)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Pulcerová, Simona
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoká škola báňská - Technická univerzita Ostrava / Ekonomická fakulta
http://linked.open...dnocenehoVysledku	120461
http://linked.open...ai/riv/idVysledku	RIV/61989100:27510/12:86084248
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	transcendence, infinite product (en)
http://linked.open.../riv/klicoveSlovo	infinite product transcendence
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[74B6596EE62B]
http://linked.open...i/riv/nazevZdroje	Czechoslovak Mathematical Journal
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Diophantine approximation of infinite sequences Distribution and metric properties of number sequences and their applications IT4Innovations Centre of Excellence
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	62
http://linked.open...iv/tvurceVysledku	Hančl, Jaroslav Pulcerová, Simona Štěpnička, Jan Kolouch, Ondřej
http://linked.open...ain/vavai/riv/wos	000310085400003
http://linked.open...n/vavai/riv/zamer	Logické a algebraické metody pro zpracování informací zatížených neurčitostí a jejich použití ve fuzzy modelování
issn	0011-4642
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s10587-012-0053-2
http://localhost/t...ganizacniJednotka	27510
is http://linked.open...avai/riv/vysledek of	A note on the transcendence of infinite products

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