Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes, decidedly flat manifolds. In our main results, we fix the value of one coordinate in Euclidean space and describe the set of points in the fiber over that fixed coordinate that are rationally approximable at a given rate. We identify translated coordinate hyperplanes for which there is a dichotomy as in Khintchine's Theorem: the set of rationally approximable points is null or full, according to the convergence or divergence of the series associated to the desired rate of approximation.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
243-273
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Department of Mathematics, University of York, Heslington, York, UK
- Department of Mathematics and Computer Science, Wesleyan University, 265 Church Street, Middletown, CT 06459, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-3-3