Diagonal quartic surfaces with a Brauer-Manin obstruction

被引：2

作者：

Santens, Tim ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium

来源：

COMPOSITIO MATHEMATICA | 2023年 / 159卷 / 04期

关键词：

quartic surfaces; rational points; Brauer-Manin obstruction; Artin L-series; HASSE PRINCIPLE; POINTS; NUMBER;

D O I：

10.1112/S0010437X22007916

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the quantity of diagonal quartic surfaces a(0)X(0)(4) + a(1)X(1)(4) + a(2)X(2)(4) + a(3)X(3)(4) = 0 which have a Brauer-Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the quantity of such surfaces ordered by height. The proof uses a generalization of a method of Heath-Brown on sums over linked variables. We also show that there exists no uniform formula for a generic generator in this family.

引用

页码：659 / 710

页数：53

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