In this talk, I described the arithmetic properties of singular values of Ramanujan's continued fraction R(q); in particular, I showed that they are algebraic units that generate specific class fields. I described a method to compute singular values "exactly" as appropriate roots of the modular polynomials satisfied by R(q), and explained how this is computationally much easier than the corresponding task for the classical j function, due to the remarkably small size of the coefficients of the modular polynomials satisfied by R.

It turns out that computing singular values of R(q) (and indeed any modular function) is best done via Shimura reciprocity and high-precision numerical calculations with q-expansions, as in A.C.P. Gee, M. Honsbeek, "Singular values of the Rogers-Ramanujan continued fraction, KdV Report 99-18, 1999" (apparantly to appear in The Ramanujan Journal)