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Computing isolated coefficients of the $j$-function

Fredrik Johansson
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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 $n = 457871$.
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Dates and versions

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



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