Generalised Weber Functions
ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
MORAIN, François
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
MORAIN, François
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
< Reduce
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Language
en
Article de revue
This item was published in
Acta Arithmetica. 2014, vol. 164, n° 4, p. 309-341
Instytut Matematyczny PAN
English 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 ...Read more >
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.Read less <
English Keywords
Weber function
complex multiplication
class invariant
European Project
Algorithmic Number Theory in Computer Science
Origin
Hal imported