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A summation formula for divisor functions associated to lattices
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Published/Copyright:
February 27, 2007
Abstract
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 GL2n, 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 GL2n(ℝ) are principal tools.
Received: 2005-03-17
Published Online: 2007-02-27
Published in Print: 2006-11-20
© Walter de Gruyter
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Articles in the same Issue
- A summation formula for divisor functions associated to lattices
- On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces
- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
- Homotopy localization of groupoids
- A group-theoretic characterization of the direct product of a ball and a Euclidean space
- Degree-regular triangulations of the double-torus
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