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Journal Articles Acta Arithmetica Year : 2014

Generalised Weber Functions

Abstract

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 $j(z)$. Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use.
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Dates and versions

inria-00385608 , version 1 (19-05-2009)
inria-00385608 , version 2 (20-12-2013)

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Cite

Andreas Enge, François Morain. Generalised Weber Functions. Acta Arithmetica, 2014, 164 (4), pp.309-341. ⟨10.4064/aa164-4-1⟩. ⟨inria-00385608v2⟩
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