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

Abstract

We study a modular function ${\Lambda }_{k,\ell }$ which is one of generalized $\lambda$ functions. We show ${\Lambda }_{k,\ell }$ and the modular invariant function $j$ generate the modular function field with respect to the modular subgroup ${\Gamma }_1(N)$. Further we prove that ${\Lambda }_{k,\ell }$ is integral over $\mathbf{Z}[j]$. From these results, we obtain that the value of ${\Lambda }_{k,\ell }$ at an imaginary quadratic point is an algebraic integer and generates a ray class field over the Hilbert class field.

In this paper, we generalize the results in the paper(arXiv:1110.4429v1[math.NT]20 Oct 2011)

References in corpus (1)

• Singular values of some modular functions

Cited by in corpus (1)

• Generators of modular function fields obtained from generalized lambda functions