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Irrationality and transcendence of continued fractions with algebraic integers

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Irrationality and transcendence of continued fractions with algebraic integers. / Andersen, Simon Bruno; Kristensen, Simon.

In: Publicationes mathematicae-Debrecen, Vol. 95, No. 3-4, 2019, p. 469-476.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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Andersen, SB & Kristensen, S 2019, 'Irrationality and transcendence of continued fractions with algebraic integers', Publicationes mathematicae-Debrecen, vol. 95, no. 3-4, pp. 469-476. https://doi.org/10.5486/PMD.2019.8575

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Andersen, Simon Bruno ; Kristensen, Simon. / Irrationality and transcendence of continued fractions with algebraic integers. In: Publicationes mathematicae-Debrecen. 2019 ; Vol. 95, No. 3-4. pp. 469-476.

Bibtex

@article{7306eee0e8394b3ebdf0300d13d17a57,
title = "Irrationality and transcendence of continued fractions with algebraic integers",
abstract = "We extend a result of Han{\v c}l, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence {αn} of algebraic integers of degree bounded by d, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition (formula presented) implies that the continued fraction α = [0; α1, α2, . . . ] is not an algebraic number of degree less than or equal to D.",
keywords = "Algebraic integers, Continued fractions, Irrationality, Transcendence",
author = "Andersen, {Simon Bruno} and Simon Kristensen",
note = "Publisher Copyright: {\textcopyright} 2019 University of Debrecen, Institute of Mathematics. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2019",
doi = "10.5486/PMD.2019.8575",
language = "English",
volume = "95",
pages = "469--476",
journal = "Publicationes mathematicae-Debrecen",
issn = "0033-3883",
publisher = "KOSSUTH LAJOS TUDOMANYEGYETEM",
number = "3-4",

}

RIS

TY - JOUR

T1 - Irrationality and transcendence of continued fractions with algebraic integers

AU - Andersen, Simon Bruno

AU - Kristensen, Simon

N1 - Publisher Copyright: © 2019 University of Debrecen, Institute of Mathematics. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

N2 - We extend a result of Hančl, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence {αn} of algebraic integers of degree bounded by d, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition (formula presented) implies that the continued fraction α = [0; α1, α2, . . . ] is not an algebraic number of degree less than or equal to D.

AB - We extend a result of Hančl, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence {αn} of algebraic integers of degree bounded by d, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition (formula presented) implies that the continued fraction α = [0; α1, α2, . . . ] is not an algebraic number of degree less than or equal to D.

KW - Algebraic integers

KW - Continued fractions

KW - Irrationality

KW - Transcendence

U2 - 10.5486/PMD.2019.8575

DO - 10.5486/PMD.2019.8575

M3 - Journal article

VL - 95

SP - 469

EP - 476

JO - Publicationes mathematicae-Debrecen

JF - Publicationes mathematicae-Debrecen

SN - 0033-3883

IS - 3-4

ER -