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On the number of rational points on a strictly convex curve. / Petrov, F. V.

в: Functional Analysis and its Applications, Том 40, № 1, 01.01.2006, стр. 24-33.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Petrov, FV 2006, 'On the number of rational points on a strictly convex curve', Functional Analysis and its Applications, Том. 40, № 1, стр. 24-33. https://doi.org/10.1007/s10688-006-0003-6

APA

Petrov, F. V. (2006). On the number of rational points on a strictly convex curve. Functional Analysis and its Applications, 40(1), 24-33. https://doi.org/10.1007/s10688-006-0003-6

Vancouver

Petrov FV. On the number of rational points on a strictly convex curve. Functional Analysis and its Applications. 2006 Янв. 1;40(1):24-33. https://doi.org/10.1007/s10688-006-0003-6

Author

Petrov, F. V. / On the number of rational points on a strictly convex curve. в: Functional Analysis and its Applications. 2006 ; Том 40, № 1. стр. 24-33.

BibTeX

@article{a20b3d3619fa48c8b522e1e0f8db7501,
title = "On the number of rational points on a strictly convex curve",
abstract = "Let γ be a bounded convex curve on the plane. Then #(γ ∩ (ℤ/n) 2) = o(n 2/3). This strengthens the classical result due to Jarn{\'i}k [J] (the upper bound cn 2/3) and disproves the conjecture on the existence of a so-called universal Jarn{\'i}k curve.",
keywords = "Affine length, Convex curve, Lattice point",
author = "Petrov, {F. V.}",
year = "2006",
month = jan,
day = "1",
doi = "10.1007/s10688-006-0003-6",
language = "English",
volume = "40",
pages = "24--33",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - On the number of rational points on a strictly convex curve

AU - Petrov, F. V.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - Let γ be a bounded convex curve on the plane. Then #(γ ∩ (ℤ/n) 2) = o(n 2/3). This strengthens the classical result due to Jarník [J] (the upper bound cn 2/3) and disproves the conjecture on the existence of a so-called universal Jarník curve.

AB - Let γ be a bounded convex curve on the plane. Then #(γ ∩ (ℤ/n) 2) = o(n 2/3). This strengthens the classical result due to Jarník [J] (the upper bound cn 2/3) and disproves the conjecture on the existence of a so-called universal Jarník curve.

KW - Affine length

KW - Convex curve

KW - Lattice point

UR - http://www.scopus.com/inward/record.url?scp=33644897337&partnerID=8YFLogxK

U2 - 10.1007/s10688-006-0003-6

DO - 10.1007/s10688-006-0003-6

M3 - Article

AN - SCOPUS:33644897337

VL - 40

SP - 24

EP - 33

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 1

ER -

ID: 49850509