Involve: A Journal of Mathematics

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

A generalization of modular forms

Adam Haque

Full-text: Open access

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.

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


Export citation

References

  • T. M. Apostol, Modular functions and Dirichlet series in number theory, 2nd ed., Graduate Texts in Mathematics 41, Springer, New York, 1990.
  • T. Jech, Set theory, 2nd ed., Springer, Berlin, 1997.
  • K. Ono, The web of modularity: arithmetic of the coefficients of modular forms and $q$-series, CBMS Regional Conference Series in Mathematics 102, American Mathematical Society, Providence, RI, 2004.
  • G. Shimura, Elementary Dirichlet series and modular forms, Springer, New York, 2007.