Certain aspects of holomorphic function theory on some genus zero arithmetic groups

Jay Jorgenson, Lejla Smajlović, Holger Then

Research output: Contribution to journalArticle (Academic Journal)

5 Citations (Scopus)

Abstract

There are a number of fundamental results in the study of holomorphic function theory associated to the discrete group PSL(2,Z) , including the following statements: the ring of holomorphic modular forms is generated by the holomorphic Eisenstein series of weights four and six, denoted by E4 and E6 ; the smallest-weight cusp form Δ has weight twelve and can be written as a polynomial in E4 and E6 ; and the Hauptmodul j can be written as a multiple of E34 divided by Δ . The goal of the present article is to seek generalizations of these results to some other genus-zero arithmetic groups Γ0(N)+ with square-free level N , which are related to ‘Monstrous moonshine conjectures’. Certain aspects of our results are generated from extensive computer analysis; as a result, many of the space-consuming results are made available on a publicly accessible web site. However, we do present in this article specific results for certain low-level groups.
Original languageEnglish
Pages (from-to)360-381
Number of pages22
JournalLMS Journal of Computation and Mathematics
Volume19
Issue number2
Early online date1 Mar 2017
DOIs
Publication statusPublished - 2017

Keywords

  • Mathematics - Number Theory

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