The density of rational points on a certain singular cubic surface

TD Browning

doi:10.1016/j.jnt.2005.11.007

The density of rational points on a certain singular cubic surface

TD Browning

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

9 Citations (Scopus)

Abstract

We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface xyz=w(x+y+z)^2, has order of magnitude B(log B)^6. This agrees with Manin's conjecture.

Translated title of the contribution	The density of rational points on a certain singular cubic surface
Original language	English
Pages (from-to)	242 - 283
Number of pages	42
Journal	Journal of Number Theory
Volume	119 (2)
DOIs	https://doi.org/10.1016/j.jnt.2005.11.007
Publication status	Published - Aug 2006

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Publisher: Academic Press
Other identifier: IDS number 076QX

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10.1016/j.jnt.2005.11.007

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title = "The density of rational points on a certain singular cubic surface",

abstract = "We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface xyz=w(x+y+z)\textasciicircum{}2, has order of magnitude B(log B)\textasciicircum{}6. This agrees with Manin's conjecture.",

author = "TD Browning",

note = "Publisher: Academic Press Other identifier: IDS number 076QX",

year = "2006",

month = aug,

doi = "10.1016/j.jnt.2005.11.007",

language = "English",

volume = "119 (2)",

pages = "242 -- 283",

journal = "Journal of Number Theory",

issn = "1096-1658",

publisher = "Academic Press Inc.",

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T1 - The density of rational points on a certain singular cubic surface

AU - Browning, TD

N1 - Publisher: Academic Press Other identifier: IDS number 076QX

PY - 2006/8

Y1 - 2006/8

N2 - We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface xyz=w(x+y+z)^2, has order of magnitude B(log B)^6. This agrees with Manin's conjecture.

AB - We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface xyz=w(x+y+z)^2, has order of magnitude B(log B)^6. This agrees with Manin's conjecture.

U2 - 10.1016/j.jnt.2005.11.007

DO - 10.1016/j.jnt.2005.11.007

M3 - Article (Academic Journal)

SN - 1096-1658

VL - 119 (2)

SP - 242

EP - 283

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

The density of rational points on a certain singular cubic surface

Abstract

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