ON THE CONGRUENT NUMBER PROBLEM OVER INTEGERS OF CYCLIC NUMBER FIELDS

被引：1

作者：

Zinevicius, Albertas ^{[1
,2
]}

机构：

[1] Vilnius Univ, Dept Math & Informat, Naugarduko 24, LT-03225 Vilnius, Lithuania

[2] Inst Math & Informat, Akad 4, LT-08663 Vilnius, Lithuania

来源：

MATHEMATICA SLOVACA | 2016年 / 66卷 / 03期

关键词：

congruent numbers; cyclic extensions; rings of integers; prime numbers;

D O I：

10.1515/ms-2015-0158

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a cyclic field extension K/Q of degree d and a nonzero rational integer m, we show that the equation mp(2) = x(4) - y(2) has no nontrivial solutions in O-K when p belongs to a subset of rational prime numbers of relative density at least phi(d)/(2d). (C) 2016 Mathematical Institute Slovak Academy of Sciences

引用

页码：561 / 564

页数：4

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