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 15h asked Show $\int_0^\infty \frac{\sin ax \sin bx}{x^2} \, dx = \frac{\pi a}{2}$ if $a < b$ Apr 8 asked show that $\sum P(x,y) e^{x^2 + y^2}$ is a modular form over $\Gamma_0(4)$ where $P(x,y) = x^4 - 6 x^2 y^2 + y^4$ Apr 6 asked Let $\theta(z) = \sum q^{n^2}$, is $\theta(-1/z)$ also a theta function? Apr 6 answered Intuitive explanation for why $\left(1-\frac{1}{n}\right)^n \to \frac{1}{e}$ Apr 6 asked Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p)$ Apr 4 asked Show that $SO_3(\mathbb{Z}) \simeq SO_3(\mathbb{Z}/3\mathbb{Z})$ Apr 4 asked A set such that $A$, $A+A$ have density zero but $A+A+A$ has positive density. Mar 24 answered What does algebraic number look like locally? Mar 24 asked Image of lines under the Cayley Transform $z \mapsto \frac{z-1}{z+1}$ Mar 21 asked equivalent to $A \to (C \leftrightarrow D)$ Mar 18 asked How to visualize the region $\mathbb{H}/\Gamma_0(4)$ and its cusps? Mar 11 asked Bijective proof of $\sigma_0(m) \,\sigma_0(n) = \sum_{r | (m,n)} \sigma_0( mn / r^2)$? Mar 9 answered Simplify Product of sines Mar 4 answered Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real? Mar 2 asked Show that $\sum_{\mathbb{Z}/N\mathbb{Z}} f(n) g(n+r)h(n+2r) = \sum_{a \in \mathbb{Z}/N\mathbb{Z}} \hat{f}(a)\hat{g}(-2a)\hat{h}(a)$ Feb 7 asked Show that $J_n(x)$ satisfies Bessel equation $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - n^2)y = 0$ Feb 6 answered Representing a linear operator on $V$ with an element of $V \otimes V^*$ Jan 29 asked Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \$? Jan 26 answered If $[x+0.19] +[x+0.20] +[x+0.21] +\cdots [x+0.91] =546$ find the value of $[100x]$.. Jan 25 asked express as contour integral $f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}}$