Ramanujan-Göllnitz-Gordon Continued Fraction

We derive many new identities involving the Ramanujan-Göllnitz-Gordon continued fraction H(q). These include relations between H(q) and H(q ⁿ ) , which are established using modular equations of degree n. We also evaluate explicitly H(q) at for various positive integers n. Using results of M. Deuring, we show that are units for all positive integers n.     

Identities for Certain Products of Theta Functions

We derive general formulas for certain products of theta functions. Several known theta function identities follow immediately from our formulas.     

Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook

In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide proofs for many of the claims about the Rogers-Ramanujan and generalized Rogers-Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.     

On a generalization of the Dedekind–Hölder theorem

The Dedekind–Hölder theorem states that Ramanujan’s sum and the Von Sterneck function are identical. In this article, we extend the Dedekind–Hölder theorem by generalizing both Ramanujan’s sum and the Von Sterneck function and showing that the two generalizations are identical.