Abstract
A complex-valued function F(z) of the complex variable z is said to be a modular function, if it is meromorphic for lm z>0, and F(Mz) = F(z) for all transformations M belonging to the modular group (defined in § 5 of Chapter I), or for all M belonging to a sub-group of the modular group of finite index.
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© 1985 Springer-Verlag Berlin Heidelberg
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Chandrasekharan, K. (1985). The modular function J(τ). In: Elliptic Functions. Grundlehren der mathematischen Wissenschaften, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52244-4_6
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DOI: https://doi.org/10.1007/978-3-642-52244-4_6
Publisher Name: Springer, Berlin, Heidelberg
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