## Arithmetic of Ramanujan's continued Fraction

We identify Ramanujan's continued fraction R(q) with a generator for the function field of the genus 0 modular
curve X(5) and use methods of Deuring and Shimura to establish arithmetic properties of R.
In particular, we describe the class fields generated by singular values of R and show that
these values are algebraic units. We establish "modular equations" of arbitrary degree and certain
congruence properties mod p (for p not 5) that are analogous to the Kronecker congruences for
the classical modular equations. Finally, we compute several modular equations and note the remarkably
small size of their coefficients.
This work is superceded and greatly generalized in Modular Curves and Ramanujan's Continued Fraction.

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