A note on splitting quadratic forms
type: Item
instance of: scholarly article
title: A note on splitting quadratic forms
zbMATH Open document ID: 0651.10013
DOI: 10.1016/0022-314X(88)90102-3
author: Larry J. Gerstein
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let \(F\) be a global function field of characteristic not 2, and let \(R\) be a Hasse domain of \(F\) with odd class number \(h_R\). The author proves that if \(V\) is a regular quadratic \(F\)-space of dimension \(\geq 5\) and \(L\) is an \(R\)-lattice on \(V\), then \(L\) has an orthogonal splitting \(L=L_1\perp L_2\perp \cdots \perp L_t\) in which rank \(L_i=2\), for \(1\leq i\leq t-1\), and rank \(L_t\leq 4\). It improves his earlier result [Am. J. Math. 91, 106--134 (1969; Zbl 0179.08001)] which was proved under the assumption \(h_R=1\).
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 11E88
zbMATH DE Number: 4061322
zbMATH Keywords: quadratic space
zbMATH Keywords: lattice
zbMATH Keywords: class numbers of Dedekind domains
zbMATH Keywords: global function field
zbMATH Keywords: Hasse domain
zbMATH Keywords: orthogonal splitting
MaRDI profile type: Publication
cites work: Splitting Quadratic Forms Over Integers of Global Fields
cites work: Unimodular quadratic forms over global function fields
cites work: Q5607309
cites work: The construction of indecomposable positive definite quadratic forms.
description: scientific article; zbMATH DE number 4061322