Size of regulators and consecutive square-free numbers

被引：5
|
作者：
Fouvry, Etienne [1 ]
Jouve, Florent [1 ]
机构：
[1] Univ Paris 11, CNRS, Math Lab, UMR 8628, F-91405 Orsay, France
来源：
MATHEMATISCHE ZEITSCHRIFT | 2013年 / 273卷 / 3-4期
关键词：
EQUATION;
D O I：
10.1007/s00209-012-1035-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that, for almost all D, the fundamental solution of the associated Pell equation x (2)-Dy (2) = 1 is greater than D (1.749 center dot center dot center dot). We also show a strong link between this question and the error term in the asymptotic formula of the number of pairs of consecutive square-free numbers.
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页码：869 / 882
页数：14
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