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

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

In: LMS Journal of Computation and Mathematics, Vol. 19, No. 2, 2017, p. 360-381.

Research output: Contribution to journalArticle

Harvard

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

APA

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

Vancouver

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

Author

Jorgenson, Jay ; Smajlović, Lejla ; Then, Holger. / Certain aspects of holomorphic function theory on some genus zero arithmetic groups. In: LMS Journal of Computation and Mathematics. 2017 ; Vol. 19, No. 2. pp. 360-381.

Bibtex

@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",

}

RIS - suitable for import to EndNote

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 -