General coefficient-vanishing results associated with theta series

Shane Chern, Dazhao Tang

Published 2022-08-21Version 1

In previous literature, there are a number of sporadic coefficient-vanishing results associated with theta series. These examples suggest certain underlying patterns. By expanding theta powers as a linear combination of products of theta functions, we present two strategies that will provide a unified treatment. Our approaches rely on studying the behavior of a product of two theta series under the action of the huffing operator. Some explicit criteria are given. We may use the presented method to not only verify experimentally discovered coefficient-vanishing results, but also to generate a series of general phenomena.