Diophantine approximation by algebraic hypersurfaces and varieties
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- by Wolfgang M. Schmidt PDF
- Trans. Amer. Math. Soc. 359 (2007), 2221-2241 Request permission
Abstract:
Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about “approximation” to a point in $\mathbb {R}^{n}$ by hyperplanes defined over the rationals. That is, we seek hyperplanes with small distance from the given point. On the other hand, following Wirsing, we may ask about approximation to a real number by real algebraic numbers of degree at most $d$. The present paper deals with a common generalization of both directions, namely with approximation to a point in $\mathbb {R}^{n}$ by algebraic hypersurfaces, or more generally algebraic varieties defined over the rationals.References
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Additional Information
- Wolfgang M. Schmidt
- Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395
- Received by editor(s): October 12, 2004
- Received by editor(s) in revised form: March 10, 2005
- Published electronically: December 5, 2006
- Additional Notes: The author was partially supported by NSF DMS 0074531
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 2221-2241
- MSC (2000): Primary 11J13, 11J81, 11J82, 11J85
- DOI: https://doi.org/10.1090/S0002-9947-06-04014-1
- MathSciNet review: 2276618