Rational solutions of pairs of diagonal equations, one cubic and one quadratic

Trevor D Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
260 Downloads (Pure)

Abstract

We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument αx3+βx2. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess non-trivial integral solutions whenever the number of variables exceeds 10.
Original languageEnglish
Pages (from-to)325-356
Number of pages32
JournalProceedings of the London Mathematical Society
Volume110
Issue number2
Early online date21 Nov 2014
DOIs
Publication statusPublished - Feb 2015

Keywords

  • math.NT
  • 11D72
  • 11L15
  • 11L07
  • 11P55
  • Weyl sums
  • Hardy-Littlewood method
  • Diophantine equations

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