All congruent numbers less than 10 000
type: Item
instance of: scholarly article
title: All congruent numbers less than 10 000
zbMATH Open document ID: 0795.11012
author: Kazunari Noda
author: Hideo Wada
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-09-20T00:00:00Z
review text: The main result of this paper is the following: If \(n\) is a square-free positive integer less than 10000, then \(n\) is a congruent number if and only if \(L(E_ n,1)=0\). Here \(E_ n\) is the elliptic curve represented by \(y^ 2= x^ 3- n^ 2 x\), and \(L(E_ n,s)\) is the Hasse-Weil \(L\)- function of \(E_ n\). Using results of \textit{J. B. Tunnell} [Invent. Math. 72, 323-334 (1983; Zbl 0515.10013)] and \textit{B. H. Gross} and \textit{D. Zagier} [C. R. Acad. Sci., Paris, Sér. I 297, 85-87 (1983; Zbl 0538.14023)] the authors are able to list all congruent numbers below 10000.
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 556447
zbMATH Keywords: elliptic curve
zbMATH Keywords: Hasse-Weil \(L\)-function
zbMATH Keywords: congruent numbers
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
full work available at URL: pjaa.69.175
OpenAlex ID: W2020560071
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DOI: 10.3792/PJAA.69.175
description: scientific article; zbMATH DE number 556447