4 problems

Conjecture for $F$ on $[\sqrt{2},2]$. For $x\in[\sqrt{2},2]$,

Let $x_1,\ldots,x_n$ be independent random variables uniformly distributed in $\{-1,1\}$, and let … be a Rademacher sum with $\operatorname{Var}(X)=1$ and $0<a_i\leq a_1$ for every…

Let $X$ be a Niemeier root system and let $g\in G^X$. Let $\check{H}^X_g$ denote the vector formed by the components of $H^X_g$ indexed by $0<r<m$, and let…

Let $\Gamma_g$ be the group associated to $g\in\mathbb{M}$, and let $T^{(-1)}_{\Gamma_g}$ denote the normalized Rademacher sum attached to $\Gamma_g$. Duncan--Frenkel conjecture. T…