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Integer Points Close to Algebraic Curves
Author(s) -
Boca Florin P.,
Vâjâitu Marian,
Zaharescu Alexandru
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002812
Subject(s) - algebraic curve , mathematics , integer (computer science) , plane curve , algebraic number , family of curves , measure (data warehouse) , plane (geometry) , algebraic surface , combinatorics , pure mathematics , mathematical analysis , geometry , computer science , database , programming language
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.