The number of integer points in a family of anisotropically expanding domains; Monatshefte fur Mathematik; Vol. 178, iss. 1

The number of integer points in a family of anisotropically expanding domains; Monatshefte fur Mathematik; Vol. 178, iss. 1

Бібліографічні деталі
Parent link:Monatshefte fur Mathematik
Vol. 178, iss. 1.— 2015.— [P. 97-111]
Автор: Kordyukov Yu. A. Yuri Arkadievich
Інші автори: Yakovlev A. A. Andrey Alexandrovich
Резюме:Title screen
We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and expand in the directions, orthogonal to this subspace. We prove some estimates for the remainder, imposing additional assumptions on the boundary of the domain. We study the average remainder estimates, where the averages are taken over rotated images of the domain by a subgroup of the group SO(n)SO(n) of orthogonal transformations of the Euclidean space RnRn. Using these results, we improve the remainder estimate in the adiabatic limit formula 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 when the foliation is a linear foliation on the torus and the metric is the standard Euclidean metric on the torus.
Режим доступа: по договору с организацией-держателем ресурса
Мова:Англійська
Опубліковано: 2015
Предмети:
электронный ресурс
труды учёных ТПУ
integer points
anisotropically expanding domains
convexity
adiabatic limits
foliation
laplace operator
алгебраическое число
прямоугольный параллелепипед
адиабатический предел
асимптотическая формула Лапласа
Онлайн доступ:https://doi.org/10.1007/s00605-015-0787-7
Формат: Електронний ресурс Частина з книги
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=661580

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