A Bezoutian approach to orthogonal decompositions of trace forms or integral trace forms of some classical polynomials

Shuichi Otake

    Research output: Contribution to journalArticle

    Abstract

    As Helmke and Fuhrmann pointed out, Bezoutian approaches have been considered to be fruitful for the study of trace forms. In this article, we study orthogonal decompositions of trace forms or integral trace forms of some classical polynomials via Bezoutians. In Section 3, we give another proof of a theorem of Feit about orthogonal decompositions of trace forms of generalized Laguerre polynomials. In Section 4, we consider integral trace forms of certain irreducible trinomials and give their orthogonal decompositions explicitly. Then, in Section 5, we obtain their canonical forms over Zp the ring of p-adic integers.

    Original languageEnglish
    Pages (from-to)291-319
    Number of pages29
    JournalLinear Algebra and Its Applications
    Volume471
    DOIs
    Publication statusPublished - 2015 Apr 15

    Keywords

    • Bezoutian
    • Generalized Laguerre polynomial
    • Hermite polynomial
    • Integral trace form
    • Trace form
    • Trinomial

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Discrete Mathematics and Combinatorics
    • Geometry and Topology
    • Numerical Analysis

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