Comptes Rendus
no. 13-14
Number Theory
Integer points on cubic Thue equations
[Points entiers sur les équations cubiques de Thue]

Présenté par : Jean-Pierre Serre

Cameron L. Stewart1
1 Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 715-718.

Nous démontrons qu'il existe une infinité de formes binaires cubiques F avec contenu 1 qui sont inéquivalentes et pour lesquelles l'équation de Thue F(x,y)=m a ≫(logm)6/7 a des solutions entiers x et y pour une infinité d'entiers m.

We prove that there are infinitely many inequivalent cubic binary forms F with content 1 for which the Thue equation F(x,y)=m has ≫(logm)6/7 solutions in integers x and y for infinitely many integers m.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.018
Cameron L. Stewart 1

1 Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 
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Cameron L. Stewart. Integer points on cubic Thue equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 715-718. doi : 10.1016/j.crma.2009.04.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.018/

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[2] E. Liverance (prepared in collaboration with Cameron Stewart) Binary cubic forms with many integral points, Surikaisekikenkyusho Kokyuroku, Volume 998 (1997), pp. 93-101

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[7] J.H. Silverman Integer points on curves of genus 1, J. London Math. Soc., Volume 28 (1983), pp. 1-7

[8] C.L. Stewart Cubic Thue equations with many solutions, Internat. Math. Res. Notices (2008) (2008:rnn040-11)

[9] A. Thue Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math., Volume 135 (1909), pp. 284-305

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☆ This research was supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada.

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