论文标题
等价两个立方体的二元二元形式的总和
Equal sums of two cubes of binary quadratic forms
论文作者
论文摘要
我们对公式的所有解决方案进行完整描述，$ f_1^3 + f_2^3 = f_3^3 + f_4^3 $ for二次表格$ f_j \ in \ mathbb c [x，y] $ in \ mathbb c [x，y] $，并展示如何将Ramanujan的示例扩展到三个相等的cub cube of Cairs of Ciairs of Cairs。我们还提供了一个完整的人口普查，以计算\ Mathbb C [x，y] $的六$ p \ sextic $ p \的数量可以写成两个立方体的总和。极端示例是$ p（x，y）= xy（x^4-y^4）$，具有六个此类表示。
We give a complete description of all solutions to the equation $f_1^3 + f_2^3 = f_3^3 + f_4^3$ for quadratic forms $f_j \in \mathbb C[x,y]$ and show how Ramanujan's example can be extended to three equal sums of pairs of cubes. We also give a complete census in counting the number of ways a sextic $p \in \mathbb C[x,y]$ can be written as a sum of two cubes. The extreme example is $p(x,y) = xy(x^4-y^4)$, which has six such representations.
