Polynomials with integral coefficients, equivalent to a given polynomial

János Kollár

doi:10.1090/S1079-6762-97-00019-X

Polynomials with integral coefficients, equivalent to a given polynomial

János Kollár

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Let f(x₀, …, x_n) be a homogeneous polynomial with rational coefficients. The aim of this paper is to find a polynomial with integral coefficients F(x₀, …, x_n) which is "equivalent" to f and as "simple" as possible. The principal ingredient of the proof is to connect this question with the geometric invariant theory of polynomials. Applications to binary forms, class numbers, quadratic forms and to families of cubic surfaces are given at the end.

Original language	English (US)
Pages (from-to)	17-27
Number of pages	11
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	3
Issue number	3
DOIs	https://doi.org/10.1090/S1079-6762-97-00019-X
State	Published - Apr 8 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Class numbers
Geometric invariant theory
Hypersurfaces
Polynomials
Quadratic forms

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10.1090/S1079-6762-97-00019-X

Cite this

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AB - Let f(x0, …, xn) be a homogeneous polynomial with rational coefficients. The aim of this paper is to find a polynomial with integral coefficients F(x0, …, xn) which is "equivalent" to f and as "simple" as possible. The principal ingredient of the proof is to connect this question with the geometric invariant theory of polynomials. Applications to binary forms, class numbers, quadratic forms and to families of cubic surfaces are given at the end.

KW - Class numbers

KW - Geometric invariant theory

KW - Hypersurfaces

KW - Polynomials

KW - Quadratic forms

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Polynomials with integral coefficients, equivalent to a given polynomial

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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