Search Results

Per request of the OP, I’m reposting my comments as an answer. This is a series of observations without any references; most of these things are well known/easily shown. Normal forms. … Using De Morgan’s laws, any term can be converted to a CNF: a $\bigwedge$ of a set of clauses, each of which is a $\bigvee$ of a set of literals (= variables and their negations; we specifically allow …

I'm converting my comments to an answer. …

To convert my comment to an answer: Let $X=\mathbb H^2$ denote the hyperbolic plane and $\Gamma< \Lambda=PSL(2,\mathbb Z)$ a finite-index subgroup. …

I am converting my comments on this question into an answer because I see that they do answer the question. …

Let me convert my comment to an answer: Your expectation is false at least if the dimension of your manifold is $\ge 5$. …

To convert my comments to an answer. Consider the case of convex-cocompact nonelementary subgroups $\Gamma< PSL(2,\mathbb C)$ whose domain of discontinuity in $S^2$ is nonempty (i.e. …

(I'm converting my comment to an answer:) No, it gives you the infinite delooping of the free symmetric infinity group on the underlying space. …

[Converted from a comment into an answer, and expanded with a copy of the statement from Siegel's book.] …

This has been answered well but as a long comment I would like to say that there is a field $X$ that is bounded by a constant multiple of $|x|^{-2}$. … It is part of the Poincare Lemma (see Spivak's Calculus on Manifolds and convert from forms to vector notation; there is an exposition of that on my web page bterrell.net) that $$ f(x) = {\rm div\,}\Big …

The foundation in this answer is probably a bit weird to work in, but I think it is interesting meta-mathematically and would at least be interesting to compare other foundations too. … I described it in this comment as a "bit lazy" but figured it would still be worth it to post. Take the language of first-order set theory and add a constant symbol $\mathcal N$. …

I am converting my comment into an answer at the request of the proposer. Given $x\in L$, let $S_x=\{y\in L\, :\, y\not\geq x\}$. …

This is slightly too long for a comment, and so I'm posting it as an answer. It doesn't seem to me like there is a simple "hack" to translate Carbery-Wright to this setting. … Even more simply in your case, all you need is to convert a non-homogeneous anti-concentration statement into a homogeneous one. …

I'm converting my comments to an answer. Let $\mathrm{Par} = \{\lambda\colon \lambda \vdash n, n \geq 0\}$ denote the set of all integer partitions. …

I guess I can convert my comment to an answer. …

Sean Eberhard has already answered your question in the comments, but perhaps it's worth mentioning that one can find quite precise information about the general class of problems you are interested in … This will give that $$\sum_{n\leqslant x} 1_S(n) \asymp \frac{x}{(\log x)^{1/2}},$$ and indeed one can convert this into an asymptotic formula. …