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

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Computing isolated coefficients of the $j$-function