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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}} $