Subconvexity for additive equations: Pairs of undenary cubic forms

Joerg Brueden; Trevor D. Wooley

doi:10.1515/crelle-2012-0115

Subconvexity for additive equations: Pairs of undenary cubic forms

Joerg Brueden^*, Trevor D. Wooley

^*Corresponding author for this work

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

10 Citations (Scopus)

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Abstract

We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the expected order of magnitude.

Original language	English
Pages (from-to)	31-67
Number of pages	37
Journal	Journal für die reine und angewandte Mathematik
Volume	696
DOIs	https://doi.org/10.1515/crelle-2012-0115
Publication status	Published - Nov 2014

Keywords

WARINGS PROBLEM
ASYMPTOTIC FORMULAS
CIRCLE METHOD
3 CUBES
SUMS

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10.1515/crelle-2012-0115

undenary20120810
The final publication is available at www.degruyter.com
Accepted author manuscript, 488 KB

http://www.maths.bris.ac.uk/~matdw/undenary20120810.pdf

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title = "Subconvexity for additive equations: Pairs of undenary cubic forms",

abstract = "We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the expected order of magnitude.",

keywords = "WARINGS PROBLEM, ASYMPTOTIC FORMULAS, CIRCLE METHOD, 3 CUBES, SUMS",

author = "Joerg Brueden and Wooley, {Trevor D.}",

year = "2014",

month = nov,

doi = "10.1515/crelle-2012-0115",

language = "English",

volume = "696",

pages = "31--67",

journal = "Journal f{\"u}r die reine und angewandte Mathematik",

issn = "0075-4102",

publisher = "de Gruyter",

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TY - JOUR

T1 - Subconvexity for additive equations: Pairs of undenary cubic forms

AU - Brueden, Joerg

AU - Wooley, Trevor D.

PY - 2014/11

Y1 - 2014/11

N2 - We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the expected order of magnitude.

AB - We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the expected order of magnitude.

KW - WARINGS PROBLEM

KW - ASYMPTOTIC FORMULAS

KW - CIRCLE METHOD

KW - 3 CUBES

KW - SUMS

U2 - 10.1515/crelle-2012-0115

DO - 10.1515/crelle-2012-0115

M3 - Article (Academic Journal)

SN - 0075-4102

VL - 696

SP - 31

EP - 67

JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

ER -

Subconvexity for additive equations: Pairs of undenary cubic forms

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Keywords

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