The number of solutions of bounded height to a system of linear equations (Q1208189)
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scientific article; zbMATH DE number 166072
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The number of solutions of bounded height to a system of linear equations |
scientific article; zbMATH DE number 166072 |
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The number of solutions of bounded height to a system of linear equations (English)
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16 May 1993
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The author considers the number of solutions with height \(\leq B\) of systems of homogeneous or inhomogeneous linear equations over a number field. Explicit asymptotic estimates with error terms are given for the number of such solutions as \(B\to\infty\). The constants involved in the formulas depend on the parameters of the number field. Similar results are obtained for the number of lattice points in certain bounded domains.
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bounded height
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system of linear diophantine equations
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explicit asymptotic estimates with error terms
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number of solutions
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number of lattice points
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bounded domains
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