Modular units from quotients of Rogers-Ramanujan type $q$-series
Number Theory
2015-06-30 v1
Abstract
In [4] and [5], Folsom presents a family of modular units as higher-level analogues of the Rogers-Ramanujan -continued fraction. These units are constructed from analytic solutions to the higher-order -recurrence equations of Selberg. Here, we consider another family of modular units, which are quotients of Hall-Littlewood -series that appear in the generalized Rogers-Ramanujan type identities of [6]. In analogy with the results of Folsom, we provide a formula for the rank of the subgroup these units generate and show that their specializations at the cusp generate a subgroup of the cyclotomic unit group of the same rank. In addition, we prove that their singular values generate the same class fields as those of Folsom's units.
Keywords
Cite
@article{arxiv.1506.08313,
title = {Modular units from quotients of Rogers-Ramanujan type $q$-series},
author = {Hannah Larson},
journal= {arXiv preprint arXiv:1506.08313},
year = {2015}
}