Counting totally real units and eigenvalue patterns in ${\mathrm{SL}}_{\mathrm{n}}(\mathbb{Z})$ and ${\mathrm{Sp}}_{2n}(\mathbb{Z})$ in thin tubes

Hee Oh

For a vector $v=(v_1,\dots ,v_n)$ with $v_1>\cdots >v_n$ and $\sum v_i=0$, we study the "directional entropy" of two arithmetic objects: (1) the logarithmic embeddings of degree-$n$…