Geodesic
Rational approximation of affine coordinate subspaces of Euclidean space
Felipe A. Ramírez1 ; David S. Simmons2 ; Fabian Süess3
1Department of Mathematics and Computer Science Wesleyan University 265 Church Street Middletown, CT 06459, U.S.A.
2Department of Mathematics University of York Heslington, York YO10 5DD, UK
3University of York Department of Mathematics Heslington, York YO10 5DD, UK
Acta Arithmetica, Tome 177 (2017) no. 1, pp. 91-100
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we prove a result which depends on the dual Diophantine type of the basepoint of the subspace. These results provide evidence for the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence.
DOI : 10.4064/aa8521-8-2016
Keywords: affine coordinate subspaces dimension least euclidean space khintchine type divergence affine coordinate subspaces dimension prove result which depends dual diophantine type basepoint subspace these results provide evidence conjecture affine subspaces euclidean space khintchine type divergence

Felipe A. Ramírez  1   ; David S. Simmons  2   ; Fabian Süess  3

1 Department of Mathematics and Computer Science Wesleyan University 265 Church Street Middletown, CT 06459, U.S.A.
2 Department of Mathematics University of York Heslington, York YO10 5DD, UK
3 University of York Department of Mathematics Heslington, York YO10 5DD, UK 
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     title = {Rational approximation of affine coordinate subspaces of {Euclidean} space},
     journal = {Acta Arithmetica},
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Felipe A. Ramírez; David S. Simmons; Fabian Süess. Rational approximation of affine coordinate subspaces of Euclidean space. Acta Arithmetica, Tome 177 (2017) no. 1, pp. 91-100. doi: 10.4064/aa8521-8-2016

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