## Involve: A Journal of Mathematics

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

### A generalization of modular forms

#### Abstract

We prove a transformation equation satisfied by a set of holomorphic functions with rational Fourier coefficients of cardinality ${2}^{{\aleph}_{0}}$ 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 ${\aleph}_{0}$ for a given weight.

#### Article information

**Source**

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

**Dates**

Received: 20 July 2010

Revised: 3 July 2011

Accepted: 4 August 2011

First available in Project Euclid: 20 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.involve/1513733445

**Digital Object Identifier**

doi:10.2140/involve.2012.5.15

**Mathematical Reviews number (MathSciNet)**

MR2924310

**Zentralblatt MATH identifier**

1284.11076

**Subjects**

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

**Keywords**

generalized modular forms Dirichlet multiplication cardinality

#### Citation

Haque, Adam. A generalization of modular forms. Involve 5 (2012), no. 1, 15--24. doi:10.2140/involve.2012.5.15. https://projecteuclid.org/euclid.involve/1513733445