arXiv subjects
Publications and source records attributed to Bülent Köklüce.
In this article, we find bases for the spaces of modular forms $M_{3}(Γ_{0}(40),\left( \frac{d}{\cdot }\right) )$ for $d=-4,-8,-20\text{ and }-40.$ We then derive formulas for the number of representations of a positive integer by all the diagonal sextenary quadratic forms with coefficients $% 1,2,5$ and $10$.
In this paper, we use a modular form approach to evaluate the convolution sums $\sum_{l+42m=n}σ(l)σ(m)$, $\sum_{2l+21m=n}σ(l)σ(m),$ $\sum_{3l+14m=n}σ(l)σ(m)$ and $\sum_{6l+7m=n}σ(l)σ(m) $ for all positive integers $n\mathbf{,}$ and then use their evaluations to determine the number of representation of a positive integer $n$ by the quadratic form $x_{1}^{2} +x_{1}x_{2} +x_{2}^{2} +x_{3}^{2} +x_{3}x_{4} +x_{4}^{2} + 14(x_{5}^{2} +x_{5}x_{6} +x_{6}^{2} +x_{7}^{2} +x_{7}x_{8} +x_{8}^{2})$.