Theta series associated with certain positive definite binary quadratic forms
Volume 169 / 2015
Acta Arithmetica 169 (2015), 331-356
MSC: Primary 11E16; Secondary 11R29.
DOI: 10.4064/aa169-4-3
Abstract
Recently, P. C. Toh derived identities expressing theta series associated with fundamental idoneal discriminants in terms of generalized Lambert series. His method depends on the fact that the ring of integers of a number field is a Dedekind domain, and is not applicable to theta series associated with non-fundamental idoneal discriminants. The aim of this article is to devise methods for determining the generalized Lambert series representations of theta series associated with non-fundamental idoneal discriminants.
