Search Results

The answer is yes. This was already proved in Gabor Szegö's original paper from 1933: G. Szegö, Über gewisse Potenzreihen mit lauter positiven Koeffizienten, Mathematische Zeitschrift, Volume 37, Nu …

The second claim is false for $n=3$. Choose $\varepsilon$ small and $\delta\ll\varepsilon$. Let $A$ be the set of all points $(x,y,z)\in\mathbb R^3$ satisfying the following inequalities: $$ \begin{c …

This doesn't quite sound like the right conjecture here, because Z is known to go to infinity on the average, by Selberg's central limit theorem (see my blog post on this topic). But this is easy to …

A couple of things (I meant to just have this as a comment but it got too long): I think with regard to the first fact, a lot of people realised it all around the same time — the article by Springer w …

Polylogarithms have interesting connections in the Theory of Partitions. This is mainly because a class of generating functions for bivariate partition statistics can be approximated by polylogarithm …

$T$ is called the clique graph of $G$, see https://link.springer.com/chapter/10.1007/0-387-22444-0_5

This is a partial answer to THC's question about a "direct" way to do this. Let $X$ be a smooth projective variety such that $\omega_X$ is ample. Then there is some $m\in\mathbb N$ such that $\mathsc …

Maybe this differential topologic way of thinking the Freudenthal suspension is much more intuitive. By Pontrjagin's contruction you can identify $\pi_{n+k}(S^n)$ with equivalence classes of framed su …

More characterisations are in the book of Haim Brezis (Analyse fonctionnelle), at the appendix of Chapter 5. I will copy two of these below, toghether with the references: If $ \dim(E)\geq 2 $ and e …

Hi, I have been working with clique graphs for the last 10 years. My doctoral tesis was about clique graphs. Recently we have proved that recognizing clique graphs is an NP-complete problem. See Th …

This is an answer Bob's question after my previous answer. It doesn't fit in a comment. As a spectrum, $\mathrm{End}(H\mathbb{Z}/2)$ is known to be a product of Eilenberg-MacLane spectra, so it is th …

A connected Hausdorff manifold with more than one point has cardinality $2^{\aleph_0}$. Here's a proof sketch. For each point $x$ of the manifold, let $U_x$ be an open Euclidean neighbourhood of $x$ …

I think that not much is known. For example I don't think that we are any closer to prove Leopoldt's conjecture for a given $F$ for infinitely many $p$ than to prove it for all $p$. Here is a result …

Olivier and all, If you trust your own minds, you should better try directly and read version 2 of the proof for only CM fields, which I posted in June this years. The rest is hot wind - people may …

Ah, (quite) some fiddling with Mathematica gave a counterexample. In the notation of anon's answer, take $$ A' = \begin{pmatrix} 1 & 1 & 1 & 1 \\\\ 1 & 1 & 1 & 0 \end{pmatrix}, \qquad B = \begin{ …