## 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 $2ℵ0$ 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 $ℵ0$ for a given weight.

#### Article information

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

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

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

#### 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

#### References

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• G. Shimura, Elementary Dirichlet series and modular forms, Springer, New York, 2007.