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If  L  ⊆ ℤ  n   is a lattice of finite index, let, where the sum is over all lattices  L ′ with  L  ⊆  L ′ ⊆ ℤ  n  . Using the automorphic theory of GL 2 n  , a generalization of the Voronoi-Oppenheim summation formula is proved for these generalized divisor functions. Bessel distributions and Hankel transforms associated with the Shalika model for the degenerate principal series representations of GL 2 n  (ℝ) are principal tools.

A summation formula for divisor functions associated to lattices