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Let $z \in \mathbb{C} \backslash \lbrace 1 \rbrace$ with $|z| = 1$. We consider the following infinite series, which necessarily converges: $$S(z) := \sum_{n = 1}^{\infty}\frac{z^n}{n}$$ Note that $S(...

Much of the literature on analysis in metric spaces makes use of an assumption called Ahlfors regularity or Ahlfors-David regularity. Let $q>0$. A metric space $(X,d)$ is Ahlfors(-David) $q$-...

We have a two sets of vectors ($\mathbb{C}^d$), $A=\{ v_1, \ldots v_n\}$ and $B=\{u_1, \ldots u_n\}$. The question is if there is an efficient solution (polynomial in $n$) for checking whether $A$ ...