Integer Points Close to Algebraic Curves | Zendy

Boca Florin P. | Zendy; Vâjâitu Marian | Zendy; Zaharescu Alexandru | Zendy

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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.

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