In this talk, I will give a quick comparison of two of our recent works that involve similar setup. We study two of Ramanujan's continued fractions and evaluate them at certain arguments in the field $K=\mathbb{Q}(\sqrt{-d})$ where the respective ideals $(2)$ and $(3)$ split into a product of prime ideals. These values are then shown to generate certain class fields over $\mathbb{Q}$. The same values are shown to be periodic points of a fixed algebraic function, independent of $d$. These are analogues of similar results for the Rogers-Ramanujan continued fraction.

Bio: Akkarapakam earned his doctorate from Purdue University, Indianapolis in 2023, under the supervision of Patrick Morton. Since then he is working as a Visiting Asst. Professor at University of Missouri-Columbia. His research is primarily in algebraic number theory, and concerns Ramanujan's continued fractions, periodic points of algebraic functions, modular identities and some class field theory.