Generalised Weber Functions. I

Details Generalised Weber Functions. I Generalised Weber Functions. I

2009-05-20

arxiv.org/abs/0905.3250v1

Mathematics

Number Theory

Scientific paper

A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to N=2. We classify the cases where some power $\w_N^e$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $\w_N(z)$ and $j(z)$.

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