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INTEGER POINTS CLOSE TO ALGEBRAIC CURVES

Published online by Cambridge University Press:  06 March 2002

FLORIN P. BOCA
Affiliation:
Institute of Mathematics, Romanian Academy, PO Box 1-764, Bucharest 70700, Romania; marian.vajaitu@imar.ro Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA; fboca@math.uiuc.edu, zaharesc@math.uiuc.edu
MARIAN VÂJÂITU
Affiliation:
Institute of Mathematics, Romanian Academy, PO Box 1-764, Bucharest 70700, Romania; marian.vajaitu@imar.ro
ALEXANDRU ZAHARESCU
Affiliation:
Institute of Mathematics, Romanian Academy, PO Box 1-764, Bucharest 70700, Romania; marian.vajaitu@imar.ro Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA; fboca@math.uiuc.edu, zaharesc@math.uiuc.edu
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Abstract

For any algebraic curve with unbounded branches in the plane, two numbers in [0, ∞] are defined that measure how closely to the curve it is possible to find infinitely many integer points. These numbers are shown to be 1 for almost all such curves. The state of the art in estimating these numbers for several classes of curves is also discussed.

Type
Research Article
Copyright
2002 London Mathematical Society

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