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

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 Felt 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 Z(p) the ring of p-adic integers. (C) 2015 Elsevier Inc. All rights reserved.