On S-Hardy-Littlewood homogeneous spaces

Masanori Morishita, Takao Watanabe

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the asymptotic distribution of S-integral points on affine homogeneous spaces in the light of the Hardy-Littlewood property introduced by Borovoi and Rudnick. We introduce the S-Hardy-Littlewood property for affine homogeneous spaces defined over an algebraic number field and a finite set S of places of the base field. We work with the adelic harmonic analysis on affine algebraic groups over a number field to determine the asymptotic density of S-integral points under congruence conditions. We give some new examples of strongly or relatively S-Hardy-Littlewood homogeneous spaces over number fields. As an application, we prove certain asymptotically uniform distribution property of integral points on an ellipsoid defined by a totally positive definite tenary quadratic form over a totally real number field.

Original languageEnglish
Pages (from-to)723-757
Number of pages35
JournalInternational Journal of Mathematics
Volume9
Issue number3
DOIs
Publication statusPublished - Sep 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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