Replication formulae for \(n| h\)-type Hauptmoduls
type: Item
instance of: scholarly article
title: Replication formulae for \(n| h\)-type Hauptmoduls
zbMATH Open document ID: 0920.11027
author: Charles R. Ferenbaugh
published in: Journal of Algebra
publication date: 1999-03-08T00:00:00Z
review text: In Monstrous Moonshine, to each of the 172 conjugacy classes of cyclic subgroups of the Monster, \(\mathbb M\), corresponds a Hauptmodul and its \(q\)-expansion at its cusp at {infinity}. There are necessarily relations among the infinitely many \(q\)-coefficients of the series, these are called replication formulae. There is also the important replication power map which maps a Hauptmodul \(f_{\langle g\rangle}\) to \(f_{\langle g^k\rangle}\). The groups of the title are described and Hauptmoduln given, and shown to satisfy the replication formulae. A consequence is that the \(q\)-coefficients are generalized characters of \(\mathbb M\). This work should be compared with the unpublished [\textit{M. Koike}, On the replication formulae and Hecke operators (Nagoya University Preprint) (1987)].
Mathematics Subject Classification ID: 11F22
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 11F06
zbMATH DE Number: 868022
zbMATH Keywords: cyclic subgroups of the Monster
zbMATH Keywords: Hauptmodul
zbMATH Keywords: replication formulae
zbMATH Keywords: \(q\)-coefficients
MaRDI profile type: Publication
full work available at URL: jabr.1996.0038
OpenAlex ID: W2064009474
DOI: 10.1006/JABR.1996.0038
description: scientific article; zbMATH DE number 868022