Integer points on the dilation of a subanalytic surface

J Pila

doi:10.1093/qmath/hag047

Integer points on the dilation of a subanalytic surface

J Pila

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

46 Citations (Scopus)

Abstract

Let Omega subset ofR(n) be a compact subanalytic set of dimension 2 and tgreater than or equal to1. This paper gives an upper bound as t-->infinity for the number of integer points on the homothetic dilation tOmega of Omega that do not reside on any connected semialgebraic subset of tOmega of positive dimension. Implications for the density of rational points on Omega are also elaborated.

Translated title of the contribution	Integer points on the dilation of a subanalytic surface
Original language	English
Pages (from-to)	207 - 223
Number of pages	17
Journal	Quarterly Journal of Mathematics
Volume	55 (2)
DOIs	https://doi.org/10.1093/qmath/hag047
Publication status	Published - Jun 2004

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Publisher: Oxford University Press
Other identifier: IDS Number: 818AX

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10.1093/qmath/hag047

http://qjmath.oxfordjournals.org/cgi/content/abstract/55/2/207

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title = "Integer points on the dilation of a subanalytic surface",

abstract = "Let Omega subset ofR(n) be a compact subanalytic set of dimension 2 and tgreater than or equal to1. This paper gives an upper bound as t-->infinity for the number of integer points on the homothetic dilation tOmega of Omega that do not reside on any connected semialgebraic subset of tOmega of positive dimension. Implications for the density of rational points on Omega are also elaborated.",

author = "J Pila",

note = "Publisher: Oxford University Press Other identifier: IDS Number: 818AX ",

year = "2004",

month = jun,

doi = "10.1093/qmath/hag047",

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T1 - Integer points on the dilation of a subanalytic surface

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N1 - Publisher: Oxford University Press Other identifier: IDS Number: 818AX

PY - 2004/6

Y1 - 2004/6

N2 - Let Omega subset ofR(n) be a compact subanalytic set of dimension 2 and tgreater than or equal to1. This paper gives an upper bound as t-->infinity for the number of integer points on the homothetic dilation tOmega of Omega that do not reside on any connected semialgebraic subset of tOmega of positive dimension. Implications for the density of rational points on Omega are also elaborated.

AB - Let Omega subset ofR(n) be a compact subanalytic set of dimension 2 and tgreater than or equal to1. This paper gives an upper bound as t-->infinity for the number of integer points on the homothetic dilation tOmega of Omega that do not reside on any connected semialgebraic subset of tOmega of positive dimension. Implications for the density of rational points on Omega are also elaborated.

U2 - 10.1093/qmath/hag047

DO - 10.1093/qmath/hag047

M3 - Article (Academic Journal)

VL - 55 (2)

SP - 207

EP - 223

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

ER -

Integer points on the dilation of a subanalytic surface

Abstract

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