A generalization of a theorem of Birch

David B. Leep, Colin L. Starr

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize a theorem of Birch on solving systems of homogeneous equations of odd degree to the case of solving systems of homogeneous equations of degree not divisible by a fixed integer s ≥ 2. Birch's theorem is the case s = 2. In addition, we give a new exposition of the proof of Brauer's theorem on solving systems of homogeneous equations.

Original languageEnglish
Pages (from-to)2640-2648
Number of pages9
JournalCommunications in Algebra
Volume37
Issue number8
DOIs
StatePublished - Aug 2009

Keywords

  • Birch's theorem
  • Systems of homogeneous equations

ASJC Scopus subject areas

  • Algebra and Number Theory

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