Quadratic diophantine equations and orders in quaternion algebras
Quadratic diophantine equations and orders in quaternion algebras
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DOI：
10.1353/ajm.2006.0016
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发表时间：
2006-03
影响因子：
1.7
通讯作者：
G. Shimura
中科院分区：
文献类型：
--
作者：
G. Shimura
本文首先用偶Clifford群重新表述了我们最近在书中给出的关于二次丢番图方程的主要定理。在四元数的情况下，群是四元数代数的乘法群，并且重新表述的定理将二次方程的一类原始解与代数中的一类阶连接起来。在不确定的情况下，每个类本质上是一类二元厄米特形式。在确定的情况下，结果是一个类似的结果高斯的总和的三个平方。
We first reformulate the main theorem on quadratic Diophantine equations given in our recent book in terms of the even Clifford group. In the quaternary case the group is the multiplicative group of a quaternion algebra, and the reformulated theorem connects a class of primitive solutions of a quadratic equation with a class of an order in the algebra. In the indefinite case each class is essentially a class of binary hermitian forms. In the definite case the result is an analogue of the result of Gauss on the sums of three squares.