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

Institut for Matematiske Fag

1 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Journal of the London Mathematical Society
Vol/bind	92
Udgave nummer	3
Sider (fra-til)	760-777
Antal sider	18
ISSN	0024-6107
DOI	https://doi.org/10.1112/jlms/jdv048
Status	Udgivet - 3 feb. 2015

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10.1112/jlms/jdv048

J. London Math. Soc.-2015-Tanimoto-760-77Forlagets udgivne version, 408 KB

Citationsformater

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

Abstract

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Citationsformater

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