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On the measure of
primitive representations of an integer by a quadratic
form
Manabu Murata |
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Vol. 344 (2026), No. 1, 69–102
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Abstract |
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We explicitly compare a measure defined by Siegel with a mass defined by Shimura, both in the context of primitive representations of an integer by an indefinite integral quadratic form. The main result gives an explicit formula for the Siegel’s measure under the assumption that the lattices are maximal. The result is applied to the computation of these measures in some families, such as that of hyperbolic forms. |
Keywords
quadratic Diophantine equation, quadratic form, primitive
representation
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Mathematical Subject Classification
Primary: 11D09, 11E12
Secondary: 11E20
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Milestones
Received: 8 February 2025
Revised: 14 April 2026
Accepted: 11 May 2026
Published: 10 August 2026
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Authors |
| Manabu Murata | |
| Department of Electrical and
Electronic Engineering Ritsumeikan University Kusatsu Japan |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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