Quadratic polynomials represented by norm forms

被引：14

作者：

Browning, T. D. ^{[1
]}

Heath-Brown, D. R. ^{[2
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[2] Univ Oxford, Inst Math, Oxford OX1 3LB, England

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2012年 / 22卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

POINTS; NUMBER; BRAUER;

D O I：

10.1007/s00039-012-0168-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P(t) is an element of Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P(t). Let N-K/Q(x)be a full norm form for the K/Q extension. We show that the variety P(t) = N-K/Q(x) not equal 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.

引用

页码：1124 / 1190

页数：67

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