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

DOI10.1016/j.laa.2015.01.005zbMath1360.11064OpenAlexW2075607041MaRDI QIDQ2261543

Shuichi Otake

Publication date: 6 March 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.01.005

zbMATH Keywords

Hermite polynomialBezoutiantrace formtrinomialgeneralized Laguerre polynomialintegral trace form

Mathematics Subject Classification ID

Quadratic forms over global rings and fields (11E12) Algebraic numbers; rings of algebraic integers (11R04) Quadratic and bilinear forms, inner products (15A63) Matrices of integers (15B36) Toeplitz, Cauchy, and related matrices (15B05) Quadratic forms over local rings and fields (11E08)

Related Items (2)

Some remarks on the non-real roots of polynomials ⋮ On the discriminant of certain quadrinomials

Cites Work

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• \(\tilde A_5\) and \(\tilde A_7\) are Galois groups over number fields
• Factorization of polynomials over finite fields
• Trace forms of trinomials
• Bézoutians
• A polynomial approach to linear algebra
• Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of \(p\)-adic integers
• A canonical quadratic form for the ring of 2-adic integers
• The Additive Characters of the Witt Ring of an Algebraic Number Field
• Discriminants of number fields defined by trinomials

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