A generalization of modular forms

Haque, Adam

doi:10.2140/involve.2012.5.15

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A generalization of modular forms

Adam Haque

Vol. 5 (2012), No. 1, 15–24

DOI: 10.2140/involve.2012.5.15

Abstract

We prove a transformation equation satisfied by a set of holomorphic functions with rational Fourier coefficients of cardinality $2^{ℵ_{0}}$ 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 $ℵ_{0}$ 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

Vol. 5, No. 1, 2012