Integer points close to algebraic curves

Florin P. Boca; Marian Vâjâitu; Alexandru Zaharescu

doi:10.1112/S0024610701002812

Integer points close to algebraic curves

Florin P. Boca, Marian Vâjâitu, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	10-26
Number of pages	17
Journal	Journal of the London Mathematical Society
Volume	65
Issue number	1
DOIs	https://doi.org/10.1112/S0024610701002812
State	Published - 2002

ASJC Scopus subject areas

General Mathematics

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10.1112/S0024610701002812

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title = "Integer points close to algebraic curves",

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.",

author = "Boca, {Florin P.} and Marian V{\^a}j{\^a}itu and Alexandru Zaharescu",

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AU - Zaharescu, Alexandru

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Integer points close to algebraic curves

Abstract

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