Integral points on cubic hypersurfaces

TD Browning; DR Heath-Brown

Integral points on cubic hypersurfaces

TD Browning, DR Heath-Brown

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

Abstract

Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension

Translated title of the contribution	Integral points on cubic hypersurfaces
Original language	English
Title of host publication	Analytic Number Theory: Essays in Honour of Klaus Roth
Editors	WWL Chen, WT Gowers, H Halberstam, WM Schmidt, RC Vaughan
Publisher	Cambridge University Press
Volume	In Press
ISBN (Print)	9780521515382
Publication status	Accepted/In press - 2007

Bibliographical note

Other identifier: 0521515386

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http://arxiv.org/abs/math/0611086

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title = "Integral points on cubic hypersurfaces",

abstract = "Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p\textasciicircum{}k is soluble for all prime powers p\textasciicircum{}k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension ",

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

note = "Other identifier: 0521515386",

year = "2007",

language = "English",

isbn = "9780521515382",

volume = "In Press",

editor = "WWL Chen and WT Gowers and H Halberstam and WM Schmidt and RC Vaughan",

booktitle = "Analytic Number Theory: Essays in Honour of Klaus Roth",

publisher = "Cambridge University Press",

address = "United Kingdom",

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TY - CHAP

T1 - Integral points on cubic hypersurfaces

AU - Browning, TD

AU - Heath-Brown, DR

N1 - Other identifier: 0521515386

PY - 2007

Y1 - 2007

N2 - Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension

AB - Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension

M3 - Chapter in a book

SN - 9780521515382

VL - In Press

BT - Analytic Number Theory: Essays in Honour of Klaus Roth

A2 - Chen, WWL

A2 - Gowers, WT

A2 - Halberstam, H

A2 - Schmidt, WM

A2 - Vaughan, RC

PB - Cambridge University Press

ER -

Integral points on cubic hypersurfaces

Abstract

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