Vol. 5, No. 1, 2012

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A generalization of modular forms

Adam Haque

Vol. 5 (2012), No. 1, 15–24
Abstract

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.

Keywords
generalized modular forms, Dirichlet multiplication, cardinality
Mathematical Subject Classification 2000
Primary: 11F11, 11F30
Milestones
Received: 20 July 2010
Revised: 3 July 2011
Accepted: 4 August 2011
Published: 28 April 2012

Communicated by Ken Ono
Authors
Adam Haque
Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104
United States