On reduced positive definite ternary quadratic forms. (Q2585804)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On reduced positive definite ternary quadratic forms. |
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On reduced positive definite ternary quadratic forms. (English)
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1940
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Die positiv definite reelle ternäre quadratische Form \[ f (x) = a_1x_1^2 +a_2x_2^2 +a_3x_3^2+2b_1x_2x_3+2b_2x_1x_3+2b_3x_1x_2 \] heißt reduziert, wenn die Ungleichungen \(0<a_1\leqq a_2\leqq a_3, 0\leqq b_1\leqq \tfrac12a_2,\) \(|b_2|\leqq \tfrac12a_1, 0\leqq b_3\leqq\tfrac12a_1,\) \(b_1-b_2+b_3\leqq \tfrac12(a_1+a_2)\) gelten. Neuer Beweis für die Abschätzung \(a_1a_2a_3\leqq 2D\), wo \(D = a_1a_2a_3-(a_1b^2_1 + a_2b_2^2 +a_3b_3^2 - 2b_1b_2b_3)\) die Determinante von \(f(x)\) ist.
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