The distribution of prime ideals of imaginary quadratic fields

被引：6

作者：

Harman, G ^{[1
]}

Kumchev, A

Lewis, PA

机构：

[1] Royal Holloway Univ London, Dept Math, Egham TW20 0EX, Surrey, England

[2] Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada

[3] Cardiff Univ, Sch Math, Cardiff CF24 4YH, S Glam, Wales

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2004年 / 356卷 / 02期

关键词：

D O I：

10.1090/S0002-9947-03-03104-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Q(x, y) be a primitive positive definite quadratic form with integer coefficients. Then, for all (s, t) is an element of R-2 there exist (m, n) is an element of Z(2) such that Q(m, n) is prime and Q(m - s, n - t) << Q(s, t)(0.53) + 1. This is deduced from another result giving an estimate for the number of prime ideals in an ideal class of an imaginary quadratic number field that fall in a given sector and whose norm lies in a short interval.

引用

页码：599 / 620

页数：22

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