This work is a correction to a paper of the same title by Ahmet Tekcan [5].
📌 3 Key Takeaways
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Objective & Hypothesis:In this study M1(G 0(3) ,c -3) , M2(G0(5), c 5) and M3(G 0(7),c -7) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x12+3x1x2+x22, 5(x12+x1x2+x1x3+x1x4+x22+x2x3+ x2x4+x32+x3x4)+2x42, and 7(x12+x1x2+x1x3+x1x4+x1x5+x22+x2x3+x2x4+x2x5+ x32+x3x4+x3x5+x42+x4x5+x52+7(x1x6+x2x6+x3x6+ x4x6+x5x6)+3x62, are determined.
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Key Findings & Data:In this study M1(G 0(3) ,c -3) , M2(G0(5), c 5) and M3(G 0(7),c -7) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x12+3x1x2+x22, 5(x12+x1x2+x1x3+x1x4+x22+x2x3+ x2x4+x32+x3x4)+2x42, and 7(x12+x1x2+x1x3+x1x4+x1x5+x22+x2x3+x2x4+x2x5+ x32+x3x4+x3x5+x42+x4x5+x52+7(x1x6+x2x6+x3x6+ x4x6+x5x6)+3x62, are determined.
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Conclusion & Impact:This work is a correction to a paper of the same title by Ahmet Tekcan [5].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Key words: Quadratic forms · representation numbers · theta series
Abstract
In this study M1(G 0(3) ,c -3) , M2(G0(5), c 5) and M3(G 0(7),c -7) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x12+3x1x2+x22, 5(x12+x1x2+x1x3+x1x4+x22+x2x3+ x2x4+x32+x3x4)+2x42, and 7(x12+x1x2+x1x3+x1x4+x1x5+x22+x2x3+x2x4+x2x5+ x32+x3x4+x3x5+x42+x4x5+x52+7(x1x6+x2x6+x3x6+ x4x6+x5x6)+3x62, are determined. This work is a correction to a paper of the same title by Ahmet Tekcan [5].
Özet
In this study M1(G 0(3) ,c -3) , M2(G0(5), c 5) and M3(G 0(7),c -7) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x12+3x1x2+x22, 5(x12+x1x2+x1x3+x1x4+x22+x2x3+ x2x4+x32+x3x4)+2x42, and 7(x12+x1x2+x1x3+x1x4+x1x5+x22+x2x3+x2x4+x2x5+ x32+x3x4+x3x5+x42+x4x5+x52+7(x1x6+x2x6+x3x6+ x4x6+x5x6)+3x62, are determined. This work is a correction to a paper of the same title by Ahmet Tekcan [5].
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