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### Proof of a result by Zhang in Artin's seminal paper

In his seminal paper, Some open problems on three-dimensional graded domains, M. Artin proposed a very small list of possible division rings of fractions that can appear as 'noncommutative function ...
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### Central limit theorem for irrational rotations

Let $\alpha$ be an algebraic integer of modulus 1, and $R_\alpha z=\alpha z$. Is $$\lim_{n\to\infty}\frac{\log|\sum_{k=1}^n \Re R_\alpha^k z|}{\log n}=\frac12$$ for all $z\in S^1$? Birkhoff's ergodic ...
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### Truncating the high degree part of a positive boolean function doesn't change the distance to positive functions too much

Given $n\in\mathbb{Z}^{+}$, suppose $f:\{-1,1\}^n\to[0,1],$ then $f$ has a Fourier expansion: $f(x)=\sum_{S\subseteq[n]} \tilde{f}(S)x^S,$ where $x^S=\prod_{i\in S}x_i,$ $\tilde{f}(S)\in\mathbb{R}$. ...
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### Reference for application of local cohomology to complex manifolds with points removed

Reference request - I am looking at Dolbeault cohomology on compact complex manifolds (not Riemann surfaces) with points removed. I have been told that the key to doing this is to look at Local ...
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A (finite) hypergraph is a pair $(V, \mathcal{E})$ where $V$ is a finite set of vertices and $\mathcal{E}\subseteq\mathcal{P}(V)$ with each $E\in\mathcal{E}$ having at least two elements; a ...