Computing isolated coefficients of the $j$-function - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2020

Computing isolated coefficients of the $j$-function

Abstract

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 $n = 457871$.
Fichier principal
Vignette du fichier
paper.pdf (185.51 Ko) Télécharger le fichier

Dates and versions

hal-03030172 , version 1 (29-11-2020)

Identifiers

Cite

Fredrik Johansson. Computing isolated coefficients of the $j$-function. 2020. ⟨hal-03030172⟩
361 View
144 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More