On pairs of diagonal quintic forms

ST Parsell, TD Wooley

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

3 Citations (Scopus)

Abstract

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy-Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.
Translated title of the contributionOn pairs of diagonal quintic forms
Original languageEnglish
Pages (from-to)61 - 96
Number of pages36
JournalCompositio Mathematica
Volume131 (1)
DOIs
Publication statusPublished - Mar 2002

Bibliographical note

Publisher: Kluwer Academic Publ

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