6 problems

Let $G$ and $G'$ be the symmetry groups specified in the claim, and write $M_G(a,b,c)_{-1}$ and $A_G(a,b,c)_{-1}$ for the corresponding matrices specialized at $q=-1$. Let…

Mészáros's critical-distribution conjecture. For every finite abelian $p$-group $G$,

Let $p$ be a prime, let $(\nu_{\alpha})_{\alpha\in\mathbb{R}}$ be a proposed one-parameter family of distributions on the set of finite abelian $p$-groups, and let $n_1<n_2<\dots$…

Let $P(t) \in \mathbb{Z}_p[t]$ be a non-constant monic square-free polynomial, written as … where each $P_j(t)\in\mathbb{Z}_p[t]$ is monic and its reduction $\bar{P}_j(t)$ modulo…

Let $X_m:=\{x_1,\ldots,x_m\}$ be a finite ordered subset of $\mathbb{Z}_p$ whose elements have distinct reductions modulo $p$, and let…

Fix finitely many monic polynomials $P_{1}(t),\dots,P_{l}(t)\in\mathbb{Z}_{p}[t]$ whose images in $\mathbb{F}_{p}[t]$ modulo $p$ are distinct and irreducible. For $1\leq j\leq l$,…