Generalised Weber Functions
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ENGE, Andreas | |
| hal.structure.identifier | Geometry, arithmetic, algorithms, codes and encryption [GRACE] | |
| hal.structure.identifier | Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX] | |
| dc.contributor.author | MORAIN, François | |
| dc.date.accessioned | 2024-04-04T02:20:34Z | |
| dc.date.available | 2024-04-04T02:20:34Z | |
| dc.date.issued | 2014 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189502 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Instytut Matematyczny PAN | |
| dc.subject.en | Weber function | |
| dc.subject.en | complex multiplication | |
| dc.subject.en | class invariant | |
| dc.title.en | Generalised Weber Functions | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4064/aa164-4-1 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 0905.3250 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | Acta Arithmetica | |
| bordeaux.page | 309-341 | |
| bordeaux.volume | 164 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00385608 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00385608v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Acta%20Arithmetica&rft.date=2014&rft.volume=164&rft.issue=4&rft.spage=309-341&rft.epage=309-341&rft.au=ENGE,%20Andreas&MORAIN,%20Fran%C3%A7ois&rft.genre=article |
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