On S-Hardy-Littlewood homogeneous spaces

Masanori Morishita, Takao Watanabe

研究成果: ジャーナルへの寄稿記事

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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.

元の言語英語
ページ(範囲)723-757
ページ数35
ジャーナルInternational Journal of Mathematics
9
発行部数3
出版物ステータス出版済み - 9 1998
外部発表Yes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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