Computing isolated coefficients of the j-function

2020/11/30 by Fredrik Johansson, Johansson, Fredrik
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2011.14671

openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of efficiently computing isolated coefficients c_n in the Fourier series of the elliptic modular function j(τ). 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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