Generalised Weber functions

• Autorzy: Andreas Enge , François Morain
• Języki publikacji: EN

Abstrakty

EN

A generalised Weber function is given by $𝔴_N(z) = η(z/N)/η(z)$, where η(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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 4
• Strony: 309-341

Daty

wydano

2014

Twórcy

autor

Andreas Enge

• INRIA, LFANT, Univ. Bordeaux, IMB, CNRS, IMB, UMR 5251, 33400 Talence, France

autor

François Morain

• INRIA Saclay-Île-de-France, École polytechnique, 91128 Palaiseau Cedex, France
• LIX (CNRS/UMR 7161), École polytechnique, 91128 Palaiseau Cedex, France

Identyfikatory

DOI

10.4064/aa164-4-1