Convergence Properties of the Classical and Generalized Rogers-Ramanujan Continued Fractions

The aim of this talk is to present some new results about the convergence and divergence of the classical and generalized Rogers-Ramanujan continued fractions on the unit circle, obtained during the Cologne Young Researchers in Number Theory Program 2015. We provide an example of an uncountable set of measure zero on which the Rogers-Ramanujan continued fraction R(x) diverges and which enlarges a set previously found by Bowman and Mc Laughlin. We further study the generalized Rogers-Ramanujan continued fractions R_a(x) for roots of unity a and give explicit convergence and divergence conditions, extending some work of Huang and Schur.
 This is joint work with Robert A. Neiss (University of Cologne)