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

Larson, Hannah

doi:10.1090/proc/13085

Modular units from quotients of Rogers-Ramanujan type $q$-series
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Proc. Amer. Math. Soc. 144 (2016), 4169-4182 Request permission

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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