Asymptotic Formulae for Pairs of Diagonal Cubic Equations

Joerg Bruedern*, Trevor D. Wooley

*Corresponding author for this work

Research output: Contribution to journalArticle (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 languageEnglish
Pages (from-to)38-54
Number of pages17
JournalCanadian Journal of Mathematics . Journal Canadien de Mathematiques
Volume63
Issue number1
DOIs
Publication statusPublished - Feb 2011

Keywords

  • exponential sums
  • Diophantine equations
  • WARING PROBLEM
  • CUBES
  • FORMS

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