Diophantine inequalities and quasi-algebraically closed fields

Craig V. Spencer*, Trevor D. Wooley

*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.

Original languageEnglish
Pages (from-to)721-738
Number of pages18
JournalIsrael Journal of Mathematics
Volume191
Issue number2
DOIs
Publication statusPublished - Oct 2012

Keywords

  • CUBIC EQUATIONS
  • THEOREM

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