cactus314
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# 160 Questions

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### show quadratic forms $x^2 + y^2 + z^2$ and $x^2 - y^2 - z^2$ are equivalent over finite fields $\mathbb{F}_p$

may 24 at 14:34 cactus314 11.3k

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### Show $\int_0^\infty \frac{\sin ax \sin bx}{x^2} \, dx = \frac{\pi a}{2}$ if $a < b$

may 3 at 16:29 cactus314 11.3k

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### 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 at 20:13 cactus314 11.3k
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### Let $\theta(z) = \sum q^{n^2}$, is $\theta(-1/z)$ also a theta function?

may 14 at 11:45 J. M. 51.7k
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### Bijective proof of $\sigma_0(m) \,\sigma_0(n) = \sum_{r | (m,n)} \sigma_0( mn / r^2)$?

mar 11 at 14:21 cactus314 11.3k
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### Show that $\sum_{\mathbb{Z}/N\mathbb{Z}} f(n) g(n+r)h(n+2r) = \sum_{a \in \mathbb{Z}/N\mathbb{Z}} \hat{f}(a)\hat{g}(-2a)\hat{h}(a)$

mar 2 at 14:47 cactus314 11.3k

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### 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 7 at 18:15 cactus314 11.3k
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### Show $\mathbb{F}_2[x]/(x^3 + x^2 + 1) \simeq \mathbb{F}_2[t]/(t^3 + t + 1)$

jan 19 at 17:53 cactus314 11.3k

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### How to write the Adeles over $\mathbb{Q}(i)$?

dec 29 at 15:37 cactus314 11.3k
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### What is the series expansion of reciprocal of theta function $\frac{1}{\theta(z;q)}$?

dec 31 at 23:36 Nemo 745

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