For d >= 4, primitive rank-(d-1) subgroups of Z^d with fixed covolume T become equidistributed toward a rotation-invariant 'polar' measure as T grows along admissible subsequences, extending Aka-Einsiedler-Shapira.
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On the distribution of primitive subgroups of $\mathbb{Z}^{d}$ of large covolume
For d >= 4, primitive rank-(d-1) subgroups of Z^d with fixed covolume T become equidistributed toward a rotation-invariant 'polar' measure as T grows along admissible subsequences, extending Aka-Einsiedler-Shapira.