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# 171 Questions

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### Why is $\theta(m) \propto \zeta(2)$ if it is counting lattice points in a hyperbola?

jul 21 at 16:27 user1952009 3,203

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### can we have probabilistic interpretation of $L(1,( \frac{\cdot }{ p}))^{-1}$

jul 12 at 19:27 cactus314 11.6k

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### Extend $g(z)$ holomorphically from $\mathrm{Re}(z) > 0$ to $\mathrm{Re}(z) \geq 0$.

jul 11 at 13:58 cactus314 11.6k

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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. 52.2k

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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 11.6k
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### proof that $\frac{x^p - 1}{x-1} = 1 + x + \dots + x^{p-1}$ is irreducible

apr 24 at 12:02 san 6,877

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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 11.6k
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### Kloosterman Sums and Lattice Hyperbolas

apr 6 at 23:09 cactus314 11.6k

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### sum of divisors function $\sum \tau(n) = \frac{1}{4}$

mar 20 at 2:18 Gerben 104

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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 11.6k
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