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Points near real algebraic sets


Authors: W. M. Schmidt and U. Zannier
Journal: Proc. Amer. Math. Soc. 142 (2014), 4127-4132
MSC (2010): Primary 11G35, 11G99; Secondary 11P21
Published electronically: August 15, 2014
MathSciNet review: 3266983
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Abstract: Given a real algebraic set $ X$ and a box $ \mathscr {B}$ in $ \mathbb{R}^n$, which is a union of cubes of equal size and with disjoint interiors, we bound the number of cubes that intersect $ X$. As a consequence, we bound the volume of the set of points having distance at most $ \delta $ from $ X \cap \mathscr {B}$, and we estimate the number of integer points in a domain $ \mathscr {D} \subset \mathbb{R}^n$ bounded by algebraic hypersurfaces.


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Additional Information

W. M. Schmidt
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395

U. Zannier
Affiliation: Scuola Normale Superiore, Piazza de Cevalier, 56100 Pisa, Italy

DOI: https://doi.org/10.1090/S0002-9939-2014-12172-1
Keywords: Points near algebraic sets, lattice points in semialgebraic sets
Received by editor(s): June 26, 2012
Received by editor(s) in revised form: February 6, 2013
Published electronically: August 15, 2014
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.