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

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

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

Companion: Equidistribution of primitive quartic torus packets for arbitrary orders evidence for this event

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. parent of this event

Lean solution module OAI/NumberTheory/DukePrimeDegree/MainUnconditional.lean evidence for this event

Lean Comparator challenge DukePrimeDegree (not in formalization.yaml) evidence for this event

Companion: Equidistribution of primitive sextic torus packets evidence for this event

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

Einsiedler, Lindenstrauss, Michel, Venkatesh, Duke's theorem for cubic fields, Annals 173 (2011) evidence for this event

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