The Ramanujan Journal

, Volume 33, Issue 1, pp 121–130 | Cite as

Special values of generalized \(\mathbf{\lambda}\) functions at imaginary quadratic points



We study a modular function Λ k, that is one of generalized λ functions. We show that Λ k, 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, is integral over Z[j]. From this result we obtain that a value of Λ k, 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)

11F03 11G15 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.KyotoJapan

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