A generalization of a theorem of Birch

David B. Leep; Colin L. Starr

doi:10.1080/00927870902747381

A generalization of a theorem of Birch

David B. Leep
, Colin L. Starr

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	2640-2648
Number of pages	9
Journal	Communications in Algebra
Volume	37
Issue number	8
DOIs	https://doi.org/10.1080/00927870902747381
State	Published - Aug 2009

Keywords

Birch's theorem
Systems of homogeneous equations

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870902747381

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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.",

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AB - 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.

KW - Birch's theorem

KW - Systems of homogeneous equations

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UR - https://www.scopus.com/pages/publications/70449486702#tab=citedBy

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JO - Communications in Algebra

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IS - 8

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A generalization of a theorem of Birch

Abstract

Keywords

ASJC Scopus subject areas

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