### 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 language | English |
---|---|

Pages (from-to) | 291-319 |

Number of pages | 29 |

Journal | Linear Algebra and Its Applications |

Volume | 471 |

DOIs | |

Publication status | Published - 2015 Apr 15 |

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### 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

### Cite this

**A Bezoutian approach to orthogonal decompositions of trace forms or integral trace forms of some classical polynomials.** / Otake, Shuichi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A Bezoutian approach to orthogonal decompositions of trace forms or integral trace forms of some classical polynomials

AU - Otake, Shuichi

PY - 2015/4/15

Y1 - 2015/4/15

N2 - 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.

AB - 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.

KW - Bezoutian

KW - Generalized Laguerre polynomial

KW - Hermite polynomial

KW - Integral trace form

KW - Trace form

KW - Trinomial

UR - http://www.scopus.com/inward/record.url?scp=84922694603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922694603&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2015.01.005

DO - 10.1016/j.laa.2015.01.005

M3 - Article

VL - 471

SP - 291

EP - 319

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -