Quadratic polynomials represented by norm forms

被引：13
|
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.
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页码：1124 / 1190
页数：67
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