Everest, G and Ward, T orcid.org/0000-0002-8253-5767 (2011) A repulsion motif in Diophantine equations. American Mathematical Monthly, 118 (7). 7. pp. 584-598. ISSN 0002-9890
Abstract
Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a nonsingular plane cubic equation has only finitely many integral solutions. Examples show that simple equations can have inordinately large integral solutions in comparison to the size of their coefficients. Nonetheless, a conjecture of Hall suggests a bound on the size of integral solutions in terms of the coefficients of the defining equation. It turns out that a similar phenomenon seems, conjecturally, to be at work for solutions which are close to being integral in another sense. We describe this conjecture as an illustration of an underlying motif—repulsion—in the theory of Diophantine equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2011, the American Mathematical Society. This is an author produced version of an article published in The American Mathematical Monthly. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Sep 2019 15:48 |
Last Modified: | 12 Sep 2019 04:48 |
Published Version: | https://www.tandfonline.com/toc/uamm20/118/7?nav=t... |
Status: | Published |
Publisher: | Taylor and Francis |
Identification Number: | 10.4169/amer.math.monthly.118.07.584 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109022 |