Polynomials with integral coefficients, equivalent to a given polynomial

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)17-27
Number of pages11
JournalElectronic Research Announcements of the American Mathematical Society
Volume3
Issue number3
DOIs
StatePublished - Apr 8 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Class numbers
  • Geometric invariant theory
  • Hypersurfaces
  • Polynomials
  • Quadratic forms

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