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：

暂无

中图分类号：

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.

引用

页码：557 / 567

页数：10

共 8 条

[1]

Estermann T.(1931)Einige Sätze über quadratfreie Zahlen Math. Ann. 105 653-662

[2]

Estermann T.(1962)A new application of the Hardy–Littlewood–Kloosterman method Proc. Lond. Math. Soc. 12 425-444

[3]

Filaseta M.(1994)Powerfree values of binary forms J. Number Theory 49 250-268

[4]

Greaves G.(1992)Power-free values of binary forms Q. J. Math. 43 45-65

[5]

Heath-Brown D.R.(1984)The square sieve and consecutive square-free numbers Math. Ann. 266 251-259

[6]

Hooley C.(2009)On the power-free values of polynomials in two variables: II J. Number Theory 129 1443-1455

[7]

Poonen B.(2003)Squarefree values of multivariable polynomials Duke Math. J. 118 353-373

[8]

Tolev D.(2005)On the exponential sum with squarefree numbers Bull. Lond. Math. Soc. 37 827-834

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