The invariant class of a binary form
type: Item
instance of: scholarly article
title: The invariant class of a binary form
zbMATH Open document ID: 1038.11073
DOI: 10.1016/S1631-073X(02)00021-3
author: Denis Simon
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-02-19T00:00:00Z
review text: The author considers how irreducible binary forms of any degree \(n\) over a ring \(R\) could be made to correspond to an ideal class in the field \(K\) of the root, so as to be invariant under \(\text{SL}(2,\mathbb{R})\). In analogy with the quadratics, a module of basis elements in \(K\) corresponds uniquely to an ideal class (but neither biuniquely when \(n> 3\) nor surjectively when \(n> 2\) , as shown by examples). The author's earlier work is cited here [\textit{D. Simon}, Indag. Math., New Ser. 12, 505--517 (2001; Zbl 1020.11065)]. The classical reference for \(n= 3\) is \textit{B. N. Delone} and \textit{D. K. Faddeev} [Theory of irrationalities of the third degree (Russian), Tr. Mat. Inst. Steklov. 11 (1940; JFM 61.0090.01)].
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11E76
zbMATH DE Number: 1907814
zbMATH Keywords: binary forms of higher degree
MaRDI profile type: Publication
cites work: Q3996190
cites work: Classical invariants and 2-descent on elliptic curves
cites work: Q5838513
cites work: The index of nonmonic polynomials
Recommended article: Invariants of Binary Forms
Recommended article: Invariants of binary forms
Recommended article: The invariant theory of binary forms
Recommended article: Q3809937
Recommended article: Matrix invariants of binary forms
Recommended article: Invariants of binary bilinear forms modulo two
Recommended article: The invariants of the binary nonic
Recommended article: A Classification of Non-Degenerated Binary Forms
description: scientific article; zbMATH DE number 1907814