3 problems

Let $N(r)$ denote the order of the outer automorphism group of the principal arithmetic subgroup $\Lambda_0^n$, in the setting of the arithmetic quotients considered in the paper.…

Let $K^{C}_{n+1}$ be the complete signed graph with $n+1$ vertices, containing all edges $(i,j,\pm)$ for $1\leq i<j\leq n+1$ and $(i,i,+)$ for $1\leq i\leq n$, and let…

Two-value minimizer conjecture. The minimum of $F(a)$ without changing the signs of $a_j$ is attained at a vector of the form $\tilde a=(\xi,\dots,\xi,\eta,\dots,\eta)$, for some…