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# Generalised Weber Functions. I

1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
3 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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 $j(z)$.
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Preprints, Working Papers, ...
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https://hal.inria.fr/inria-00385608
Contributor : Andreas Enge <>
Submitted on : Tuesday, May 19, 2009 - 4:28:57 PM
Last modification on : Monday, May 20, 2019 - 2:30:25 PM
Long-term archiving on: : Thursday, June 10, 2010 - 9:33:21 PM

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weber.pdf
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### Identifiers

• HAL Id : inria-00385608, version 1
• ARXIV : 0905.3250

### Citation

Andreas Enge, François Morain. Generalised Weber Functions. I. 2009. ⟨inria-00385608v1⟩

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