Exceptional integers for genera of integral ternary positive definite quadratic forms
type: Item
instance of: scholarly article
title: Exceptional integers for genera of integral ternary positive definite quadratic forms
zbMATH Open document ID: 0948.11019
DOI: 10.1215/S0012-7094-00-10227-X
published in: Duke Mathematical Journal
publication date: 2000-11-27T00:00:00Z
review text: Let \((L,q)\) be a \(\mathbb{Z}\)-lattice of rank 3 with integral positive definite quadratic form. Then all sufficiently large integers that are represented primitively by some lattice in the spinor genus of \((L,q)\) are represented by all lattices in that spinor genus [\textit{W. Duke} and \textit{R. Schulze-Pillot}, Invent. Math. 99, 49-57 (1990; Zbl 0692.10020)]. The theorems of this article imply a slightly sharper characterization of the set of exceptional integers that are represented by some forms in the genus of \(L\) but not by all of them. This is explained in detail in the article under review. Furthermore the question of effectivity and results for primitive representations are described.
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11E20
zbMATH DE Number: 1436093
zbMATH Keywords: ternary quadratic forms
zbMATH Keywords: exceptional integers
zbMATH Keywords: spinor genus
author: Rainer Schulze-Pillot
reviewed by: Meinhard Peters
MaRDI profile type: Publication
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full work available at URL: s0012-7094-00-10227-x
OpenAlex ID: W2003873698
description: scientific article; zbMATH DE number 1436093