The higher-dimensional Duke theorem for torus packets of totally real fields of prime degree at least five (with primitive quartic and sextic cases)

Principal Theorem 1.1: for each fixed prime $n\ge5$ and any totally real fields $K_i$ of degree $n$ with full lattices $M_i$ whose multiplier-order discriminant $D(M_i)\to\infty$, the packet measures converge weakly to Haar measure on $X_n$ with no escape of mass, for every local homothety type, nonmaximal orders of unbounded index and every field (no exceptional set). Companions: the same for Picard packets of arbitrary orders in primitive totally real quartic fields, and for ideal-class packets of maximal orders in primitive totally real sextic fields. Not shown: individual orbits, rates, composite degrees with proper intermediate fields, nonmaximal sextic orders.

Principal Theorem 1.1: for each fixed prime $n\ge5$ and any totally real fields $K_i$ of degree $n$ with full lattices $M_i$ whose multiplier-order discriminant $D(M_i)\to\infty$, the packet measures converge weakly to Haar measure on $X_n$ with no escape of mass, for every local homothety type, nonmaximal orders of unbounded index and every field (no exceptional set). Companions: the same for Picard packets of arbitrary orders in primitive totally real quartic fields, and for ideal-class packets of maximal orders in primitive totally real sextic fields. Not shown: individual orbits, rates, composite degrees with proper intermediate fields, nonmaximal sextic orders.