• Corpus ID: 14237656

Weighted Generating Functions and Configuration Results for Type II Lattices and Codes

  title={Weighted Generating Functions and Configuration Results for Type II Lattices and Codes},
  author={Scott Duke Kominers and Noam D. Elkies and Henry Cohn and John H. Conway and B. Gross and Abhinav Kumar and Gabriele Nebe and Ken Ono},
We present an exposition of weighted theta functions, which are weighted generating functions for the norms and distribution of lattice vectors. We derive a decomposition theorem for the space of degree-d homogeneous polynomials in terms of spaces of harmonic polynomials and then prove that the weighted theta functions of Type II lattices are examples of modular forms. Our development of these results is structural, related to the infinite-dimensional representation theory of the Lie algebra… 

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