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Apr
16
accepted Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $
Apr
16
comment Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $
this did not depend on $p = 4k\pm 1$ ?
Apr
16
awarded  Nice Question
Apr
15
accepted How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?
Apr
9
reviewed Leave Open Proving that normalising a vector in $\mathbb{R}^n$ is continuous
Apr
9
reviewed Close Characterize all continuous functions such that $\int_0^1 \left(f\left(\sqrt[i]{x}\right)\right)^{k - i}\,dx = {i\over k}$
Apr
9
reviewed Leave Open Is it possible to prove that $\{\mathbb{N}\} = \{\}$?
Apr
9
reviewed Leave Open Does this iterative sequence converge?
Apr
9
reviewed Leave Open Volume Integral Discriminant
Apr
8
comment show that $\sum P(x,y) e^{x^2 + y^2}$ is a modular form over $\Gamma_0(4)$ where $P(x,y) = x^4 - 6 x^2 y^2 + y^4$
My best guess this comes from $f(x,y) = P(x,y) e^{-(x^2+y^2)}$ and saying $$ \sum_{(x,y) \in \mathbb{Z}^2} f(x,y) = \sum_{(x,y) \in \mathbb{Z}^2} \hat{f}(x,y)$$ which is Poisson summation in two variables and $\mathbb{Z}^2$ is a lattice dual to itself.
Apr
8
revised show that $\sum P(x,y) e^{x^2 + y^2}$ is a modular form over $\Gamma_0(4)$ where $P(x,y) = x^4 - 6 x^2 y^2 + y^4$
added 11 characters in body
Apr
8
revised show that $\sum P(x,y) e^{x^2 + y^2}$ is a modular form over $\Gamma_0(4)$ where $P(x,y) = x^4 - 6 x^2 y^2 + y^4$
deleted 31 characters in body
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
8
comment Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $
@anomaly covering map is fine. I reasoned for example that $\mathrm{Spin}(2) \to \mathrm{SO}_3$ is a 2-1 covering map for $\mathbb{R}$. And we have $\mathrm{Spin}_2 \simeq \mathrm{SU}_2$.
Apr
7
revised Let $\theta(z) = \sum q^{n^2}$, is $\theta(-1/z)$ also a theta function?
added 3 characters in body
Apr
6
comment Show the Dedekind $\eta(\tau)$ function is a modular form of weight $\frac{1}{2}$ for $\Gamma_0(6)$
I have read that $\eta(\tau)^24$ is a modular form of weight 12 over $\mathrm{SL}_2(\mathbb{Z})$, so maybe $\eta$ is modular of weight $\frac{1}{2}$ ?
Apr
6
revised Kloosterman Sums and Lattice Hyperbolas
added 2 characters in body
Apr
6
asked Let $\theta(z) = \sum q^{n^2}$, is $\theta(-1/z)$ also a theta function?
Apr
6
reviewed Close Subgroup half as big as its group is normal.
Apr
6
reviewed Leave Open Expand the function $e^{z+\frac{1}{z}}$ in laurent series around the origin