Generators of modular function fields obtained from generalized lambda functions

Abstract

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup. Further we study its values at imaginary quadratic points.

revised version to add results for the excluded cases;typos

References in corpus (1)

• Special values of generalized $\lambda$ functions at imaginary quadratic points