Evaluation of the convolution sums $W_{1,42}(n),$ $W_{2,21}(n),$ $W_{3,14}(n)$ and $W_{6,7}(n)$

In this paper, we use a modular form approach to evaluate the convolution sums $\sum_{l + 42 m = n} σ (l) σ (m)$ , $\sum_{2 l + 21 m = n} σ (l) σ (m),$ $\sum_{3 l + 14 m = n} σ (l) σ (m)$ and $\sum_{6 l + 7 m = n} σ (l) σ (m)$ for all positive integers $n,$ and then use their evaluations to determine the number of representation of a positive integer $n$ by the quadratic form $x_{1}^{2} + x_{1} x_{2} + x_{2}^{2} + x_{3}^{2} + x_{3} x_{4} + x_{4}^{2} + 14 (x_{5}^{2} + x_{5} x_{6} + x_{6}^{2} + x_{7}^{2} + x_{7} x_{8} + x_{8}^{2})$ .

Evaluation of the convolution sums $W_{1, 42} (n),$ $W_{2, 21} (n),$ $W_{3, 14} (n)$ and $W_{6, 7} (n)$

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Evaluation of the convolution sums $W_{1, 42} (n),$ $W_{2, 21} (n),$ $W_{3, 14} (n)$ and $W_{6, 7} (n)$

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Evaluation of the convolution sums W1,42(n),W1,42​(n), W2,21(n),W2,21​(n), W3,14(n)W3,14​(n) and W6,7(n)W6,7​(n)

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Evaluation of the convolution sums W1,42(n),W1,42​(n), W2,21(n),W2,21​(n), W3,14(n)W3,14​(n) and W6,7(n)W6,7​(n)

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Evaluation of the convolution sums $W_{1, 42} (n),$ $W_{2, 21} (n),$ $W_{3, 14} (n)$ and $W_{6, 7} (n)$

讲解博客

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Evaluation of the convolution sums $W_{1, 42} (n),$ $W_{2, 21} (n),$ $W_{3, 14} (n)$ and $W_{6, 7} (n)$

讲解博客

AI智能校验