@article{117da3886e794131a9b798a14a514579, title = "Certain aspects of holomorphic function theory on some genus zero arithmetic groups", 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.", keywords = "Mathematics - Number Theory", author = "Jay Jorgenson and Lejla Smajlović and Holger Then", year = "2017", doi = "10.1112/S1461157016000425", language = "English", volume = "19", pages = "360--381", journal = "LMS Journal of Computation and Mathematics", issn = "1461-1570", publisher = "London Mathematical Society", number = "2", }