论文标题
对角四分之一表面，带有brauer-manin障碍物
Diagonal quartic surfaces with a Brauer-Manin obstruction
论文作者
论文摘要
在本文中，我们研究了对角线四分之一的量$ a_0 x_0^4 + a_1 x_1^4 + a_2 x_2^4 + a_3 x_3^4 = 0 $，它具有brauer-manin buffsion to hasse原则。我们能够找到一个渐近公式，用于按高度排序的此类表面的数量。该证明使用链接变量对heath-brown方法的概括。我们还表明，这个家庭中的通用发电机没有统一的公式。
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.
