Probabilistic Galois theory for quartic polynomials

被引：5

作者：

Dietmann, Rainer ^{[1
]}

机构：

[1] Inst Algebra & Zahlentheorie, D-70550 Stuttgart, Germany

来源：

GLASGOW MATHEMATICAL JOURNAL | 2006年 / 48卷

关键词：

D O I：

10.1017/S0017089506003272

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there are only O(H3+epsilon) quartic integer polynomials with height at most H and a Galois group which is a proper subgroup of S-4. This improves in the special case of degree four a bound by Gallagher that yielded O(H-7/2 log H).

引用

页码：553 / 556

页数：4

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