The density of rational points on non-singular hypersurface, II

TD Browning; DR Heath-Brown

doi:10.1112/S0024611506015784

The density of rational points on non-singular hypersurface, II

TD Browning, DR Heath-Brown

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

21 Citations (Scopus)

Abstract

This paper establishes the conjecture that a non-singular projective hypersurface of dimension r, which is not equal to a linear space, contains O(B^{r+\epsilon}) rational points of height at most B, for any choice of \epsilon>0. The implied constant in this estimate depends at most upon \epsilon, r and the degree of the hypersurface.

Translated title of the contribution	The density of rational points on non-singular hypersurface, II
Original language	English
Pages (from-to)	273 - 303
Number of pages	31
Journal	Proceedings of the London Mathematical Society
Volume	93 (2)
DOIs	https://doi.org/10.1112/S0024611506015784
Publication status	Published - Sept 2006

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Publisher: London Math Soc
Other identifier: IDS number 082AW

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title = "The density of rational points on non-singular hypersurface, II",

abstract = "This paper establishes the conjecture that a non-singular projective hypersurface of dimension r, which is not equal to a linear space, contains O(B\textasciicircum{}\{r+\textbackslash{}epsilon\}) rational points of height at most B, for any choice of \textbackslash{}epsilon>0. The implied constant in this estimate depends at most upon \textbackslash{}epsilon, r and the degree of the hypersurface.",

author = "TD Browning and DR Heath-Brown",

note = "Publisher: London Math Soc Other identifier: IDS number 082AW",

year = "2006",

month = sep,

doi = "10.1112/S0024611506015784",

language = "English",

volume = "93 (2)",

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journal = "Proceedings of the London Mathematical Society",

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T1 - The density of rational points on non-singular hypersurface, II

AU - Browning, TD

AU - Heath-Brown, DR

N1 - Publisher: London Math Soc Other identifier: IDS number 082AW

PY - 2006/9

Y1 - 2006/9

N2 - This paper establishes the conjecture that a non-singular projective hypersurface of dimension r, which is not equal to a linear space, contains O(B^{r+\epsilon}) rational points of height at most B, for any choice of \epsilon>0. The implied constant in this estimate depends at most upon \epsilon, r and the degree of the hypersurface.

AB - This paper establishes the conjecture that a non-singular projective hypersurface of dimension r, which is not equal to a linear space, contains O(B^{r+\epsilon}) rational points of height at most B, for any choice of \epsilon>0. The implied constant in this estimate depends at most upon \epsilon, r and the degree of the hypersurface.

U2 - 10.1112/S0024611506015784

DO - 10.1112/S0024611506015784

M3 - Article (Academic Journal)

SN - 1460-244X

VL - 93 (2)

SP - 273

EP - 303

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

ER -

The density of rational points on non-singular hypersurface, II

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