4 problems

Let $W(E_{10})$ be the Coxeter group under consideration, and let $\rho(d4e)$ denote the spectral radius of an element $d4e\in W(E_{10})$. For each level $n$, let…

Let an arithmetic hyperbolic orbifold of the first type be a quotient of hyperbolic space by an arithmetic lattice of the first type. For a hyperbolic element $\gamma$, write…

Let $\theta_n^{-1}$ denote the relevant Perron-number sequence, and let a Salem number be a real algebraic integer greater than $1$ whose conjugates satisfy the usual Salem-number…

Let ${\rm T}$ be the set of Salem numbers, let $c>1$, and let $A_q$ denote the classes of Salem numbers used in the source. Local Density Conjecture. For every $c>1$, there exists…