The representation numbers of certain octonary quadratic forms (Q2840293)
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scientific article; zbMATH DE number 6189003
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The representation numbers of certain octonary quadratic forms |
scientific article; zbMATH DE number 6189003 |
Statements
17 July 2013
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quadratic forms
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sum of divisors functions
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convolution sums
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representation numbers
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0.97753406
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0.97714907
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0.97431266
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0.9720117
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0.9565289
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0.9425533
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0.94013333
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0.93234396
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The representation numbers of certain octonary quadratic forms (English)
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The author continues his previous paper [Int. J. Number Theory 9, No. 2, 505--516 (2013; Zbl 1273.11010)] and derives formulae for the number of representations of \(n\) by the following octonary quadratic forms NEWLINENEWLINE\[NEWLINEx_1^2+x_1x_2+x_2^2+2x_3^2+2x_3x_4+2x_4^2+2x_5^2+2x_5x_6+2x_6^2+4x_7^2+4x_7x_8+4x_8^2,NEWLINE\]NEWLINENEWLINENEWLINE\[NEWLINEx_1^2+x_1x_2+x_2^2+2x_3^2+2x_3x_4+2x_4^2+3x_5^2+3x_5x_6+3x_6^2+6x_7^2+6x_7x_8+6x_8^2,NEWLINE\]NEWLINE NEWLINENEWLINE\[NEWLINEx_1^2+x_1x_2+x_2^2+2x_3^2+2x_3x_4+2x_4^2+4x_5^2+4x_5x_6+4x_6^2+8x_7^2+8x_7x_8+8x_8^2)NEWLINE\]NEWLINENEWLINEfor any \(n\in\mathbb N_0\).
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