On the number of pairs of positive integers x, y ≤ H such that x2 + y2 + 1 is squarefree

被引：0
|
作者：
D. I. Tolev
机构：
[1] Sofia University “St. Kl. Ohridsky”,Faculty of Mathematics and Informatics
来源：
Monatshefte für Mathematik | 2012年 / 165卷
关键词：
Squarefree numbers; Kloosterman sums; 11L05; 11N25; 11N37;
D O I：
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学科分类号：
摘要：
It is not difficult to find an asymptotic formula for the number of pairs of positive integers x, y ≤ H such that x2 + y2 + 1 is squarefree. In the present paper we improve the estimate for the error term in this formula using the properties of certain exponential sums. A.Weils’s estimate for the Kloosterman sum plays the major role in our analysis.
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页码：557 / 567
页数：10
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