Singular values of multiple eta-quotients for ramified primes
| 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 | Institut für Mathematik [Augsburg] | |
| dc.contributor.author | SCHERTZ, Reinhard | |
| dc.date.accessioned | 2024-04-04T02:21:46Z | |
| dc.date.available | 2024-04-04T02:21:46Z | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 1461-1570 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189602 | |
| dc.description.abstractEn | We determine the conditions under which singular values of multiple $\eta$-quotients of square-free level, not necessarily prime to~$6$, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index $2^{k' - 1}$ when $k' \geq 2$ primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of elliptic curves with prescribed complex multiplication. The result is generalised to singular values of modular functions on $X_0^+ (p)$ for $p$ prime and ramified. | |
| dc.language.iso | en | |
| dc.publisher | London Mathematical Society | |
| dc.subject.en | complex multiplication | |
| dc.subject.en | class invariants | |
| dc.subject.en | eta quotients | |
| dc.subject.en | ring class fields | |
| dc.title.en | Singular values of multiple eta-quotients for ramified primes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/S146115701300020X | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1301.5521 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | LMS Journal of Computation and Mathematics | |
| bordeaux.page | 407-418 | |
| bordeaux.volume | 16 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00768375 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00768375v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=LMS%20Journal%20of%20Computation%20and%20Mathematics&rft.date=2013&rft.volume=16&rft.spage=407-418&rft.epage=407-418&rft.eissn=1461-1570&rft.issn=1461-1570&rft.au=ENGE,%20Andreas&SCHERTZ,%20Reinhard&rft.genre=article |
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