VANISHING COEFFICIENTS IN POWERS OF THETA FUNCTIONS WITH ODD MODULI

Abstract

Following the recent investigation of Somashekara and Thulasi on vanishing coefficients in a certain infinite $q$-product, we further study this phenomenon in a family of powers of theta functions with odd moduli, and prove that some arithmetic progressions on vanishing coefficients could be classified into a unified family, which significantly extends a result obtained by Somashekara and Thulasi.