We study a modular function Λk,ℓ that is one of generalized λ functions. We show that Λk,ℓ and the modular invariant function j generate the modular function field with respect to the modular subgroup Γ1(N). Further, we prove that Λk,ℓ is integral over Z[j]. From this result we obtain that a value of Λk,ℓ at an imaginary quadratic point is an algebraic integer and generates a ray class field over a Hilbert class field.
Modular function Special value
Mathematics Subject Classification (2010)
This is a preview of subscription content, log in to check access.
Cox, D.: Primes of the Form x2+ny2. A Wiley-Interscience Publication. Wiley, New York (1989)