Indefinite Theta Series on Cones
Number Theory
2017-01-17 v2
Abstract
We show that indefinite theta series on cones converge and provide an explicit modular completion. Our completion rests on a convolution of the Gaussian with a piecewise constant function supported on the cone. Our main innovation is to formulate this convolution in terms of euclidean geometry as opposed to hyperbolic geometry. This change of perspective allows us to establish essential asymptotic estimates without further difficulty.
Cite
@article{arxiv.1608.08874,
title = {Indefinite Theta Series on Cones},
author = {Martin Westerholt-Raum},
journal= {arXiv preprint arXiv:1608.08874},
year = {2017}
}