Abstract
We study a modular function Λ k,ℓ that is one of generalized λ functions. We show that Λ k,ℓ and the modular invariant function j generate the modular function field with respect to the modular subgroup Γ 1(N). Further, we prove that Λ k,ℓ is integral over Z[j]. From this result we obtain that a value of Λ k,ℓ at an imaginary quadratic point is an algebraic integer and generates a ray class field over a Hilbert class field.
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Ishii, N. Special values of generalized \(\mathbf{\lambda}\) functions at imaginary quadratic points. Ramanujan J 33, 121–130 (2014). https://doi.org/10.1007/s11139-013-9463-5
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DOI: https://doi.org/10.1007/s11139-013-9463-5