On the divergence of the Rogers--Ramanujan continued fraction on the Salem points - Hindov,Raul (Master's Theses in Mathematical Sciences, 2019)
The Rogers-Ramanujan continued fraction converges inside the unit circle and diverges outside of it. Its behavior on the unit circle is subtle, there is a countable dense set where it converges, a countable dense set where it diverges, and for the remaining uncountable set the question of convergence is mostly unsolved. The Bowman-McLaughlin conjecture says that we have divergence almost everywhere on the unit circle. We show some evidence for the divergence on a Salem point.
Keywords: Continued fractions; Rogers-Ramanujan; Salem numbers