## Modular Curves and Ramanujan's Continued Fraction

We use arithmetic models of modular curves to establish some properties of Ramanujan's continued fraction.
In particular, we give a new geometric proof that its singular values are algebraic units that generate specific
abelian extensions of imaginary quadratic fields, and we use a mixture of geometric and analytic methods to
construct and study an infinite family of two-variable polynomials over **Z** that are related to Ramanujan's function
in the same way that the classical modular polynomials are related to the classical j-function. We also prove that
a singular value on the imaginary axis, necessarily real, lies in a real radical tower in **R**
only if all odd prime factors of its degree over **Q** are Fermat primes; by computing some ray class groups,
we give examples where this necessary condition is not satisfied.

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