On certain ternary quadratic forms (Q1080881)
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scientific article; zbMATH DE number 3968672
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain ternary quadratic forms |
scientific article; zbMATH DE number 3968672 |
Statements
On certain ternary quadratic forms (English)
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1987
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The arithmetic of quaternion algebras is used to give a necessary and sufficient criterion for the representability of rational numbers by the form \[ Ax^ 2+By^ 2-ABz^ 2,\quad A,B\in\mathbb Z. \] As a byproduct, the well known criterion for the representability of an integer as a sum of three squares is reproved.
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quaternion algebras
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sum of three squares
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ternary quadratic forms
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representation of rationals
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representation of integers
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