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Elliptic Functions by W. F. Eberlein, J. V. Armitage

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6 Introduction to transformation theory

6.1 The elliptic modular function

In Chapter 5, we considered Equation (5.11)

m≡k2=θ24(0|τ)/θ34⁣(0|τ).(6.1)

Then we formulated the problem of determining all the solutions τ of (6.1) for a given m and in Theorem 5.2 we stated that if τ1 is one such solution then every solution is of the form

τ2=aτ1+bcτ1+d,

where a, b, c, d U+2208 U+2124, adbc = 1, a, d 1(mod ...

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