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Modular units from quotients of Rogers-Ramanujan type $ q$-series


Author: Hannah Larson
Journal: Proc. Amer. Math. Soc. 144 (2016), 4169-4182
MSC (2010): Primary 11G16; Secondary 11P84
DOI: https://doi.org/10.1090/proc/13085
Published electronically: April 27, 2016
MathSciNet review: 3531170
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Abstract: In recent work, Folsom presents a family of modular units as higher-level analogues of the Rogers-Ramanujan $ q$-continued fraction. These units are constructed from analytic solutions to the higher-order $ q$-recurrence equations of Selberg. Here, we consider another family of modular units, which are quotients of Hall-Littlewood $ q$-series that appear in the generalized Rogers-Ramanujan type identities in the work of Griffin, Ono, and Warnaar. 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 0 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.


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Additional Information

Hannah Larson
Affiliation: 5015 Donald Street, Eugene, Oregon 97405
Email: hannahlarson@college.harvard.edu

DOI: https://doi.org/10.1090/proc/13085
Received by editor(s): June 27, 2015
Received by editor(s) in revised form: November 27, 2015, and January 2, 2016
Published electronically: April 27, 2016
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2016 American Mathematical Society