On primitive solutions of quadratic Diophantine equation with four variables

JOURNAL OF NUMBER THEORY

卷:133

Article

Murata, Manabu

关键词: Quadratic form;    Quaternion algebra;    Mass formula;    Quadratic Diophantine equation;   

DOI  :  10.1016/j.jnt.2012.12.011

来源: Elsevier

【 摘 要 】

We treat certain integral lattices in ternary quadratic spaces. Each of them is described by an order associated with the lattice in the even Clifford algebra. In this viewpoint we determine the mass of the genus of such a lattice. As an application the number of primitive solutions of a quadratic Diophantine equation with four variables can be derived by means of the mass formula due to Shimura. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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