Involve: A Journal of Mathematics

  • Involve
  • Volume 5, Number 1 (2012), 15-24.

A generalization of modular forms

Adam Haque

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We prove a transformation equation satisfied by a set of holomorphic functions with rational Fourier coefficients of cardinality 20 arising from modular forms. This generalizes the classical transformation property satisfied by modular forms with rational coefficients, which only applies to a set of cardinality 0 for a given weight.

Article information

Involve, Volume 5, Number 1 (2012), 15-24.

Received: 20 July 2010
Revised: 3 July 2011
Accepted: 4 August 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight 11F30: Fourier coefficients of automorphic forms

generalized modular forms Dirichlet multiplication cardinality


Haque, Adam. A generalization of modular forms. Involve 5 (2012), no. 1, 15--24. doi:10.2140/involve.2012.5.15.

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