Simultaneous Approximation on Affine Subspaces-Reference-Cited by-同舟云学术

Simultaneous Approximation on Affine Subspaces

Published:2019-11-11 Issue:19 Volume:2021 Page:14905-14921
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Huang Jing-Jing¹^ORCID,Liu Jason J²

Affiliation:

1. Department of Mathematics and Statistics, University of Nevada, Reno, 1664 N. Virginia St., Reno, NV 89557, USA

2. Davidson Academy, 1164 N Virginia St, Reno, NV 89503, USA

Abstract

Abstract We solve the convergence case of the generalized Baker–Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the approximation function. In order to prove these results, we establish asymptotic formulae for the number of rational points close to an affine subspace. One key ingredient is a sharp upper bound on a certain sum of reciprocals of fractional parts associated with the matrix defining the affine subspace.

Funder

University of Nevada, Reno

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2021/19/14905/42269019/rnz190.pdf

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