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INTEGER POINTS CLOSE TO ALGEBRAIC CURVES

Published online by Cambridge University Press:  06 March 2002

FLORIN P. BOCA ,
MARIAN VÂJÂITU  and
ALEXANDRU ZAHARESCU
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
Information
Journal of the London Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 10 - 26
Copyright
2002 London Mathematical Society

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