Computing isolated coefficients of the $j$-function
hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
dc.contributor.author | JOHANSSON, Fredrik | |
dc.date.accessioned | 2024-04-04T02:48:42Z | |
dc.date.available | 2024-04-04T02:48:42Z | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191764 | |
dc.description.abstractEn | We consider the problem of efficiently computing isolated coefficients $c_n$ in the Fourier series of the elliptic modular function $j(\tau)$. We show that a hybrid numerical-modular method with complexity $n^{1+o(1)}$ is efficient in practice. As an application, we locate the first few values of $c_n$ that are prime, the first occurring at $n = 457871$. | |
dc.language.iso | en | |
dc.title.en | Computing isolated coefficients of the $j$-function | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
dc.identifier.arxiv | 2011.14671 | |
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-03030172 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-03030172v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=JOHANSSON,%20Fredrik&rft.genre=preprint |
Files in this item
Files | Size | Format | View |
---|---|---|---|
There are no files associated with this item. |