Computing the Hilbert Class Fields of Quartic CM Fields Using Complex Multiplication
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Mathematical institute | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | ASUNCION, Jared | |
| dc.date.accessioned | 2024-04-04T02:46:36Z | |
| dc.date.available | 2024-04-04T02:46:36Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191568 | |
| dc.description.abstractEn | Let K be a quartic CM field, that is, a totally imaginary quadratic extension of a real quadratic number field. In a 1962 article titled On the classfields obtained by complex multiplication of abelian varieties, Shimura considered a particular family {F_K(m) : m ∈ Z >0 } of abelian extensions of K, and showed that the Hilbert class field H_K of K is contained in F_K(m) for some positive integer m. We make this m explicit. We then give an algorithm that computes a set of defining polynomials for the Hilbert class field using the field F_K(m). Our proof-of-concept implementation of this algorithm computes a set of defining polynomials much faster than current implementations of the generic Kummer algorithm for certain examples of quartic CM fields. | |
| dc.language.iso | en | |
| dc.title.en | Computing the Hilbert Class Fields of Quartic CM Fields Using Complex Multiplication | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 2104.13639 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03210279 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03210279v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ASUNCION,%20Jared&rft.genre=preprint |
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