Singular values of generalized \(\lambda\) functions

We study special values of a modular function \(\Lambda\) which is one of generalized \(\lambda\) functions. We show special values of \(\Lambda\) at imaginary quadratic points are algebraic integers. Further we prove that \(\Lambda\) and the modular invariant function generate the modular function...

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Bibliographic Details
Published in:arXiv.org 2011-10
Main Author: Ishii, Noburo
Format: Article
Language:English
Subjects:
Integers
Subgroups
Online Access:Get full text
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Summary:We study special values of a modular function \(\Lambda\) which is one of generalized \(\lambda\) functions. We show special values of \(\Lambda\) at imaginary quadratic points are algebraic integers. Further we prove that \(\Lambda\) and the modular invariant function generate the modular function field with respect to the modular subgroup \(\Gamma_1(N)\).
ISSN:2331-8422