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Titel
Rational approximation to algebraic varieties and a new exponent of simultaneous approximation
VerfasserSchleischitz, Johannes
Erschienen in
Monatshefte für Mathematik, Berlin, 2016, Jg. --, S. 1-16
ErschienenSpringer, 2016
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Exponents of Diophantine approximation / Rational points on varieties / Continued fractions
ISSN1436-5081
URNurn:nbn:at:at-ubbw:3-1765 Persistent Identifier (URN)
DOI10.1007/s00605-016-0914-0 
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Rational approximation to algebraic varieties and a new exponent of simultaneous approximation [0.47 mb]
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Abstract in dt. Sprache nicht verfügbar

Zusammenfassung (Englisch)

This paper deals with two main topics related to Diophantine approximation. Firstly, we show that if a point on an algebraic variety is approximable by rational vectors to a sufficiently large degree, the approximating vectors must lie in the topological closure of the rational points on the variety. In many interesting cases, in particular if the set of rational points on the variety is finite, this closure does not exceed the set of rational points on the variety itself. This result enables easier proofs of several known results as special cases. The proof can be generalized in some way and encourages to define a new exponent of simultaneous approximation. The second part of the paper is devoted to the study of this exponent.

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