Siegel theta series for indefinite quadratic forms
arXiv:2009.08230 · doi:10.1007/s40993-021-00272-y
Abstract
The modular transformation behavior of theta series for indefinite quadratic forms is well understood in the case of elliptic modular forms due to Vignéras, who deduced that solving a differential equation of second order serves as a criterion for modularity. In this paper, we will give a generalization of this result to Siegel theta series.
v2: 23 pages, incorporating referee's comments: minor errors fixed and major structural changes