The distribution of S-integral points on SL2-orbit closures of binary forms

Sho Tanimoto; James Tanis

doi:10.1112/jlms/jdv048

The distribution of S-integral points on SL₂-orbit closures of binary forms

Sho Tanimoto, James Tanis

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

We study the distribution of S-integral points on SL2-orbit closures of binary forms and prove an asymptotic formula for the number of S-integral points. This extends a result of Duke, Rudnick and Sarnak. The main ingredients of the proof are the method of mixing developed by Eskin-McMullen and Benoist-Oh, Chambert-Loir-Tschinkel's study of asymptotic volume of height balls and Hassett-Tschinkel's description of log resolutions of {\rm SL}2-orbit closures of binary forms.

Original language	English
Journal	Journal of the London Mathematical Society
Volume	92
Issue number	3
Pages (from-to)	760-777
Number of pages	18
ISSN	0024-6107
DOIs	https://doi.org/10.1112/jlms/jdv048
Publication status	Published - 3 Feb 2015

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J. London Math. Soc.-2015-Tanimoto-760-77Final published version, 408 KB

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title = "The distribution of S-integral points on SL2-orbit closures of binary forms",

abstract = "We study the distribution of S-integral points on SL2-orbit closures of binary forms and prove an asymptotic formula for the number of S-integral points. This extends a result of Duke, Rudnick and Sarnak. The main ingredients of the proof are the method of mixing developed by Eskin-McMullen and Benoist-Oh, Chambert-Loir-Tschinkel's study of asymptotic volume of height balls and Hassett-Tschinkel's description of log resolutions of {\rm SL}2-orbit closures of binary forms.",

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AB - We study the distribution of S-integral points on SL2-orbit closures of binary forms and prove an asymptotic formula for the number of S-integral points. This extends a result of Duke, Rudnick and Sarnak. The main ingredients of the proof are the method of mixing developed by Eskin-McMullen and Benoist-Oh, Chambert-Loir-Tschinkel's study of asymptotic volume of height balls and Hassett-Tschinkel's description of log resolutions of {\rm SL}2-orbit closures of binary forms.

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The distribution of S-integral points on SL2-orbit closures of binary forms

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The distribution of S-integral points on SL₂-orbit closures of binary forms