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Cubic Thue equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2009Embargo end date: 01 Jul 2009Publisher:University of Debrecen/ Debreceni EgyetemJournal:Publicationes Mathematicae Debrecen, volume 75, pages 459-483 (issn: 0033-3883, Copyright policy )
Authors: Akhtari, S.;

doi: 10.5486/pmd.2009.4538 , 10.48550/arxiv.0907.3288

arXiv: 0907.3288

handle: 21.11116/0000-0004-2786-9 , 21.11116/0000-0004-2788-7

Cubic Thue equations

Abstract

We revisit a work by R. Okazaki and prove that for every cubic binary form F(x, y) with large enough discriminant, the Thue equation |F(x, y)| = 1 has at most 7 solutions in integers x and y.

To appear in the Publicationes Mathematicae Debrecen

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Keywords

Mathematics - Number Theory, cubic Thue equations, FOS: Mathematics, 11D25, 11J86, Thue-Mahler equations, Cubic and quartic Diophantine equations, Number Theory (math.NT), linear forms in logarithms, Linear forms in logarithms; Baker's method, Thue-Siegel method

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 6
    popularity
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    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Average
Green