Generalised Weber functions

Andreas Enge, and François Morain. "Generalised Weber functions." Acta Arithmetica 164.4 (2014): 309-341. <http://eudml.org/doc/279664>.

@article{AndreasEnge2014,
abstract = {A generalised Weber function is given by $_N(z) = η(z/N)/η(z)$, 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 $_N^e$ 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 $_N(z)$ 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.},
author = {Andreas Enge, François Morain},
journal = {Acta Arithmetica},
keywords = {complex multiplication; class invariants; eta quotients},
language = {eng},
number = {4},
pages = {309-341},
title = {Generalised Weber functions},
url = {http://eudml.org/doc/279664},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Andreas Enge
AU - François Morain
TI - Generalised Weber functions
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 4
SP - 309
EP - 341
AB - A generalised Weber function is given by $_N(z) = η(z/N)/η(z)$, 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 $_N^e$ 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 $_N(z)$ 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.
LA - eng
KW - complex multiplication; class invariants; eta quotients
UR - http://eudml.org/doc/279664
ER -