Linear relations among the Fourier coefficients of modular forms on groups Γ0 (N) of genus zero and their applications

D. Choi; Y. Choie

doi:10.1016/j.jmaa.2006.03.031

Linear relations among the Fourier coefficients of modular forms on groups Γ₀ (N) of genus zero and their applications

D. Choi, Y. Choie

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the linear relations among the Fourier coefficients of modular forms on the group Γ₀ (N) of genus zero. Applying these linear relations, congruence properties of Hecke eigenforms, replicable properties of Hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained. The eta-quotient expression of the unique normalized modular form Δ_N (z) of weight 12 on Γ₀ (N) with a zero of maximum order at ∞ is listed.

Original language	English
Pages (from-to)	655-666
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.03.031
Publication status	Published - 2007 Feb 1
Externally published	Yes

Bibliographical note

Funding Information:
The work was partially supported by KOSEF R01-2003-00011596-0 and ITRC. Corresponding author. E-mail addresses: [email protected] (D. Choi), [email protected] (Y. Choie).

Keywords

Congruences
Modular forms

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2006.03.031

Cite this

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title = "Linear relations among the Fourier coefficients of modular forms on groups Γ0 (N) of genus zero and their applications",

abstract = "We study the linear relations among the Fourier coefficients of modular forms on the group Γ0 (N) of genus zero. Applying these linear relations, congruence properties of Hecke eigenforms, replicable properties of Hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained. The eta-quotient expression of the unique normalized modular form ΔN (z) of weight 12 on Γ0 (N) with a zero of maximum order at ∞ is listed.",

keywords = "Congruences, Modular forms",

author = "D. Choi and Y. Choie",

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AU - Choi, D.

AU - Choie, Y.

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N2 - We study the linear relations among the Fourier coefficients of modular forms on the group Γ0 (N) of genus zero. Applying these linear relations, congruence properties of Hecke eigenforms, replicable properties of Hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained. The eta-quotient expression of the unique normalized modular form ΔN (z) of weight 12 on Γ0 (N) with a zero of maximum order at ∞ is listed.

AB - We study the linear relations among the Fourier coefficients of modular forms on the group Γ0 (N) of genus zero. Applying these linear relations, congruence properties of Hecke eigenforms, replicable properties of Hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained. The eta-quotient expression of the unique normalized modular form ΔN (z) of weight 12 on Γ0 (N) with a zero of maximum order at ∞ is listed.

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KW - Modular forms

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