Density of integer solutions to diagonal quadratic forms

被引：6

作者：

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

机构：

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

来源：

MONATSHEFTE FUR MATHEMATIK | 2007年 / 152卷 / 01期

关键词：

quadratic forms; Hardy-Littlewood circle method; density of solutions; uniform upper bounds;

D O I：

10.1007/s00605-007-0457-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B -> infinity. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.

引用

页码：13 / 38

页数：26

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