Schinzel Hypothesis on average and rational points

被引：6
作者：
Skorobogatov, Alexei N. [1 ,2 ]
Sofos, Efthymios [3 ]
机构：
[1] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England
[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127994, Russia
[3] Univ Glasgow, Dept Math, Univ Pl, Glasgow G12 8QQ, Lanark, Scotland
来源：
INVENTIONES MATHEMATICAE | 2023年 / 231卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
HASSE PRINCIPLE; 2; QUADRICS; PRIMES; INTERSECTIONS; PROGRESSIONS; VALUES;
D O I：
10.1007/s00222-022-01153-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Chatelet equations.
引用
收藏
页码：673 / 739
页数：67
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