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## Computing isolated coefficients of the $j$-function

Fredrik Johansson
• Function : Author
• PersonId : 1008347

#### 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 $n = 457871$.

#### Domains

Mathematics [math] Number Theory [math.NT]

### Dates and versions

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

### Identifiers

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

### Cite

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

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