Modular completions of indefinite theta series on tetrahedral cones

Holomorphic indefinite theta series are approximately the sum over the intersection of a lattice and a closed cone in the associated real quadratic space. It is necessary for convergence that this cone is non-negative. Polyhedral cones are cones which correspond to hyperbolic polyhedra in the projectivisation of the real quadratic space. They can be used to approximate all other cones, and on the other hand can be built up from tetrahedral cones. Zwegers's thesis contains the case of a 1-tetrahedron in the projectivisation of a quadratic space of signature $(n,1)$. In summer, the case of positive, rectangular cones that are positive in signature $(n,2)$ was treated.Non UBCUnreviewedAuthor affiliation: Chalmers University of TechnologyFacult