Integer points in domains and adiabatic limits

Y. A. Kordyukov, A. A. Yakovlev

Результат исследований: Материалы для журналаСтатья

2 Цитирования (Scopus)

Выдержка

An asymptotic formula is proved for the number of integral points in a family of bounded domains with smooth boundary in Euclidean space; these domains remain unchanged along some linear subspace and expand in the directions orthogonal to this subspace. A sharper estimate for the remainder is obtained in the case where the domains are strictly convex. These results make it possible to improve the remainder estimate in the adiabatic limit formula (due to the first author) for the eigenvalue distribution function of the Laplace operator associated with a bundle-like metric on a compact manifold equipped with a Riemannian foliation in the particular case where the foliation is a linear foliation on the torus and the metric is the standard Euclidean metric on the torus.

Язык оригиналаАнглийский
Страницы (с-по)977-987
Число страниц11
ЖурналSt. Petersburg Mathematical Journal
Том23
Номер выпуска6
DOI
СостояниеОпубликовано - 28 дек 2012
Опубликовано для внешнего пользованияДа

Отпечаток

Integer Points
Distribution functions
Mathematical operators
Foliation
Remainder
Metric
Torus
Subspace
Riemannian Foliation
Eigenvalue Distribution
Integral Points
Laplace Operator
Strictly Convex
Asymptotic Formula
Compact Manifold
Estimate
Expand
Euclidean space
Bounded Domain
Euclidean

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Цитировать

Integer points in domains and adiabatic limits. / Kordyukov, Y. A.; Yakovlev, A. A.

В: St. Petersburg Mathematical Journal, Том 23, № 6, 28.12.2012, стр. 977-987.

Результат исследований: Материалы для журналаСтатья

Kordyukov, Y. A. ; Yakovlev, A. A. / Integer points in domains and adiabatic limits. В: St. Petersburg Mathematical Journal. 2012 ; Том 23, № 6. стр. 977-987.
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