Research output: Contribution to journal › Article

**Certain aspects of holomorphic function theory on some genus zero arithmetic groups.** / Jorgenson, Jay; Smajlović, Lejla; Then, Holger.

Research output: Contribution to journal › Article

Jorgenson, J, Smajlović, L & Then, H 2017, 'Certain aspects of holomorphic function theory on some genus zero arithmetic groups', *LMS Journal of Computation and Mathematics*, vol. 19, no. 2, pp. 360-381. https://doi.org/10.1112/S1461157016000425

Jorgenson, J., Smajlović, L., & Then, H. (2017). Certain aspects of holomorphic function theory on some genus zero arithmetic groups. *LMS Journal of Computation and Mathematics*, *19*(2), 360-381. https://doi.org/10.1112/S1461157016000425

Jorgenson J, Smajlović L, Then H. Certain aspects of holomorphic function theory on some genus zero arithmetic groups. LMS Journal of Computation and Mathematics. 2017;19(2):360-381. https://doi.org/10.1112/S1461157016000425

@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",

}

TY - JOUR

T1 - Certain aspects of holomorphic function theory on some genus zero arithmetic groups

AU - Jorgenson, Jay

AU - Smajlović, Lejla

AU - Then, Holger

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Mathematics - Number Theory

U2 - 10.1112/S1461157016000425

DO - 10.1112/S1461157016000425

M3 - Article

VL - 19

SP - 360

EP - 381

JO - LMS Journal of Computation and Mathematics

JF - LMS Journal of Computation and Mathematics

SN - 1461-1570

IS - 2

ER -