# Computing isolated coefficients of the $j$-function

1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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 $n = 457871$.
Document type :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-03030172
Contributor : Fredrik Johansson <>
Submitted on : Sunday, November 29, 2020 - 8:35:53 PM
Last modification on : Wednesday, December 2, 2020 - 12:02:13 PM

### Identifiers

• HAL Id : hal-03030172, version 1
• ARXIV : 2011.14671

### Citation

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

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