# All Questions

7
questions with bounties

6
votes

0
answers

453
views

+50

### 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 ...

-5
votes

1
answer

450
views

+500

### 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 ...

4
votes

1
answer

148
views

+100

### Gonality of specific Riemann surfaces $y^k=\tfrac{z^k-1}{z^k+1}$

The gonality of a compact Riemann surface $\Sigma$ is defined to be the lowest degree $d$ of a non-constant holomorphic map $f\colon \Sigma\to\mathbb CP^1.$ This means the gonality is 1 only for $\...

3
votes

0
answers

80
views

+50

### Distance between solutions of differential inclusions

Suppose that we have two differential inclusions
$$\frac{dY^1}{dt}(t)\in b_1(Y^1,t)$$
with $Y^1(0)\in Y_0^1$ and
$$\frac{dY^2}{dt}(t)\in b_2(Y^2,t)$$
with $Y^2(0)\in Y_0^2$.
Can we then control $d(Y^1(...

2
votes

0
answers

117
views

+50

### 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 $x^S=\prod_{i\in S}x_i,$ $\tilde{f}(S)\in\mathbb{R}$. ...

1
vote

0
answers

101
views

+400

### 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 ...

3
votes

0
answers

119
views

+50

### Chip firing on hypergraphs

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 ...