Asymptotic Formulae for Pairs of Diagonal Cubic Equations

Joerg Bruedern; Trevor D. Wooley

doi:10.4153/CJM-2010-067-3

Asymptotic Formulae for Pairs of Diagonal Cubic Equations

Joerg Bruedern^*, Trevor D. Wooley

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.

Original language	English
Pages (from-to)	38-54
Number of pages	17
Journal	Canadian Journal of Mathematics . Journal Canadien de Mathematiques
Volume	63
Issue number	1
DOIs	https://doi.org/10.4153/CJM-2010-067-3
Publication status	Published - Feb 2011

Keywords

exponential sums
Diophantine equations
WARING PROBLEM
CUBES
FORMS

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title = "Asymptotic Formulae for Pairs of Diagonal Cubic Equations",

abstract = "We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.",

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AU - Bruedern, Joerg

AU - Wooley, Trevor D.

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N2 - We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.

AB - We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.

KW - exponential sums

KW - Diophantine equations

KW - WARING PROBLEM

KW - CUBES

KW - FORMS

U2 - 10.4153/CJM-2010-067-3

DO - 10.4153/CJM-2010-067-3

M3 - Article (Academic Journal)

SN - 0008-414X

VL - 63

SP - 38

EP - 54

JO - Canadian Journal of Mathematics . Journal Canadien de Mathematiques

JF - Canadian Journal of Mathematics . Journal Canadien de Mathematiques

IS - 1

ER -

Asymptotic Formulae for Pairs of Diagonal Cubic Equations

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