Points near real algebraic sets
HTML articles powered by AMS MathViewer
- by W. M. Schmidt and U. Zannier PDF
- Proc. Amer. Math. Soc. 142 (2014), 4127-4132 Request permission
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.References
- Riccardo Benedetti and Jean-Jacques Risler, Real algebraic and semi-algebraic sets, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1990. MR 1070358
- H. Davenport, On a principle of Lipschitz, J. London Math. Soc. 26 (1951), 179–183. MR 43821, DOI 10.1112/jlms/s1-26.3.179
- Joe Harris, Algebraic geometry, Graduate Texts in Mathematics, vol. 133, Springer-Verlag, New York, 1992. A first course. MR 1182558, DOI 10.1007/978-1-4757-2189-8
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
- MR Author ID: 186540
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 4127-4132
- MSC (2010): Primary 11G35, 11G99; Secondary 11P21
- DOI: https://doi.org/10.1090/S0002-9939-2014-12172-1
- MathSciNet review: 3266983