Polyhedral Gauss sums, and polytopes with symmetry

• Main Authors: Malikiosis, Romanos-Diogenes, Robins, Sinai, Zhang, Yichi
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2016
• Subjects: Gauss sum; lattice; Weyl group; multi-tiling; polyhedron; solid angle; Gram relations
• Online Access: https://hdl.handle.net/10356/80394; http://hdl.handle.net/10220/40540; http://arxiv.org/abs/1508.01876
• Institution: Nanyang Technological University

We define certain natural finite sums of nn'th roots of unity, called GP(n)GP(n), that are associated to each convex integer polytope PP, and which generalize the classical 11-dimensional Gauss sum G(n)G(n) defined over Z/nZZ/nZ, to higher dimensional abelian groups and integer polytopes. We...