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Jennifer Beineke, Daniel Bump

A summation formula for divisor functions associated to lattices

If L ⊆ ℤⁿ is a lattice of finite index, let , where the sum is over all lattices L′ with L ⊆ L′ ⊆ ℤⁿ. Using the automorphic theory of GL_2n, 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_2n(ℝ) are principal tools.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 18, 11/2006
Pages: 869 - 906

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