MathOverflow

I'm taking a course on topology and probability. Today, the professor remarked something along the lines of:
If you look at the space of probability distributions with $0$ mean and variance $1$, equipped with convolution, then the Gaussian distribution is characterized as the fixed point of each orbit."...

Let $k \geq 1$ and $n \geq 2$ be integers. For each prime number $p$, define$$inv_p:=\min\left\{n :\gcd(n^{p \cdot k}-1,n!-1)>1 \text{ for every } k \right\},$$provided that such a minimum exists.
Now, in his answer, Marco Mantovanelli has already shown that $inv_2$ cannot exist, since$$\gcd(n^2-1,n!-1)=1$$for every $n$....

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$, and $M$ an $R$-module. Define$$\operatorname{Supp}_R(M)\setminus V(I)=\{\mathfrak p\in \operatorname{Supp}_R(M)\mid I\nsubseteq \mathfrak p\},$$and let$$\dim(\operatorname{Supp}_R(M)\setminus...

I am trying to better understand the current obstruction to proving irrationality results for low-dimensional cyclotomic period spaces, especially Catalan’s constant $G=L(2,\chi_4).$
From a motivic/MZV perspective, $G$ appears to belong to a very small (essentially one-dimensional) Dirichlet-character eigenspace of weight $2$. This makes it feel philosophically closer to the “isolated” $\zeta(3)$-situation than to the higher-weight...