Sums-of-squares formulas over algebraically closed fields

Melissa Lynn

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of sums-of-squares formulas over algebraically closed fields is independent of the characteristic. We make the bound on p explicit, and we prove that the existence of a sums-of-squares formula of fixed type over an algebraically closed field is theoretically (though not practically) computable.

    Original languageEnglish (US)
    Pages (from-to)393-410
    Number of pages18
    JournalJournal of Algebra
    Volume497
    DOIs
    StatePublished - Mar 1 2018

    Bibliographical note

    Publisher Copyright:
    © 2017 Elsevier Inc.

    Keywords

    • Algebraic geometry
    • Gröbner bases
    • Number theory
    • Sums-of-squares formulas

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