On primitive solutions of quadratic Diophantine equation with four variables

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 D...

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Bibliographic Details
Published inJournal of number theory Vol. 133; no. 7; pp. 2431 - 2454
Main Author Murata, Manabu
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2013
Subjects
Mass formula
Quadratic Diophantine equation
Quadratic form
Quaternion algebra
Quadratic Diophantine equation
Quadratic form
Mass formula
Quaternion algebra
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Summary: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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2012.12.011