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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-3,
author = {Heng Huat Chan},
title = {Theta series associated with certain positive definite binary quadratic forms},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {331-356},
zbl = {06456776},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-3}
}
Heng Huat Chan. Theta series associated with certain positive definite binary quadratic forms. Acta Arithmetica, Tome 168 (2015) pp. 331-356. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-3/