Eisenstein series of \(3/2\) weight and one conjecture of Kaplansky
type: Item
instance of: scholarly article
title: Eisenstein series of \(3/2\) weight and one conjecture of Kaplansky
zbMATH Open document ID: 1008.11013
DOI: 10.1007/BF02877016
author: Dingyi Pei
author: Xueli Wang
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: The paper studies the problem of how to find integers represented by a positive definite ternary quadratic form. Each of the forms determines a corresponding genus of forms. Following Kaplansky, any integer represented by some forms of the genus, is called an eligible number of the genus. The paper proves that the quadratic form \(f_{1}=x^2+y^2+7z^2\) represents all eligible numbers of the genus of \(f_{1}\) congruent to \(2 \bmod 3\) except \(14 \cdot 7^{2k}\). This result was conjectured by \textit{I. Kaplansky} [Math. Comput. 64, 341-345 (1995; Zbl 0826.11015)]. The present paper also studies some analogous problems for quadratic forms of special type from two class genera.
reviewed by: Guram Gogishvili
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 1782049
zbMATH Keywords: Eisenstein series
zbMATH Keywords: genus of forms
zbMATH Keywords: eligible numbers
zbMATH Keywords: positive quadratic form
MaRDI profile type: Publication
Wikidata QID: Q122978219
cites work: The First Nontrivial Genus of Positive Definite Ternary Forms
cites work: The eligible numbers of positive definite ternary forms
description: scientific article; zbMATH DE number 1782049