Computing isolated coefficients of the $j$-function
JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Réduire
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Langue
en
Document de travail - Pré-publication
Résumé en anglais
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 ...Lire la suite >
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 $n = 457871$.< Réduire
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