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

Dohoon Choi, Y. Choie

Research output: Contribution to journalArticle

2 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 ΔN (z) of weight 12 on Γ0 (N) with a zero of maximum order at ∞ is listed.

Original languageEnglish
Pages (from-to)655-666
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume326
Issue number1
DOIs
Publication statusPublished - 2007 Feb 1
Externally publishedYes

Fingerprint

Linear Relation
Modular Forms
Fourier coefficients
Congruence
Genus
Zero
Quotient

Keywords

  • Congruences
  • Modular forms

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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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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