MathOverflow

For a negative fundamental discriminant $D$, the Chowla--Selberg gamma quotientis defined by $CS(D)=(\prod_{1\le j\le|D|}\Gamma(j/|D|)^{(D/j)})^{1/h'(D)}$, where$(D/j)$ is the kronecker symbol, and $h'(D)=h(D)/(w(D)/2)$ is the class number of $Q(\sqrt...

Let $G$ be a group. Let $p$ be a prime with $p\mid |G|$. Let $k$ be a field of characteristic $p$.
Some generalities:
Let $\mathcal{C}$ be an abelian category. Let $[X]$ denote the isomorphism class of each object $X\in\mathcal{C}$.

Is there any triple $a_1,a_2,a_3$ of distinct positive integers such that $(a_1x+1)(a_2x+1)(a_3x+1)$ is a perfect square for at least six positive integers $x$?
An example by Petričević (2023) shows that $(x+1)(55x+1)(276x+1)$ is a perfect square for at least following five positive integers: $x = 4, 8, 17, 89, 4870844$. Magma confirms that there are no other solutions in positive integers.Other known examples...

Let $n \geq 2$, and let $M^n \subset \mathbf{R}^{n+1}$ be a minimal surface with $0 \in M$ and finite ($n$-dimensional) area growth:$\operatorname{limsup}_{R \to \infty} R^{-n} \lVert M \cap B_R \rVert < \infty$. Let $\mathbf{C}_0$ be a tangent cone...