The Fourier coefficients of the McKay-Thompson series and the traces of CM values

2017/03/29 by Toshiki Matsusaka, Matsusaka, Toshiki · 1 citation
Mathematics · #11F03 #11F22 #11F30 #11F50 #11G15 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.10115

openalex publication_date 2017/03/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The elliptic modular j function enjoys many beautiful properties. Its Fourier coefficients are related to the Monster group, and its CM values generate abelian extensions over imaginary quadratic fields. Kaneko gave an arithmetic formula for the Fourier coefficients expressed in terms of the traces of the CM values. In this article, we are concerned with analogues of Kaneko's result for the McKay-Thompson series of square-free level.

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• The Fourier coefficients and singular moduli of the elliptic modular function j(τ), revisited

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