On the representation of numbers by the direct sums of some quaternary quadratic forms (Q2726699)
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scientific article; zbMATH DE number 1621371
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the representation of numbers by the direct sums of some quaternary quadratic forms |
scientific article; zbMATH DE number 1621371 |
Statements
22 November 2001
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modular forms
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integral quadratic forms
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explicit formulas
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representation numbers
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quaternary quadratic forms
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On the representation of numbers by the direct sums of some quaternary quadratic forms (English)
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The author constructs explicit bases for the spaces of cusp forms \(S_{2m} (\Gamma_0(5), \chi^m)\) and\break \(S_{2m} (\Gamma_0(13), \chi^m)\) for all integers \(m\geq 2\). Then he gets certain explicit formulas for the representation numbers by direct sums of \(m\) summands of quaternary quadratic forms of discriminant 5 (resp. 13) for \(m= 2,\dots, 6\) (resp. \(2,\dots, 5)\).
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