DOI QR코드

DOI QR Code

ON POLYNOMIAL-STRUCTURE OF RINGS OF MODULAR FORMS FOR Γ0(N)

  • Kim, Daeyeoul ;
  • Li, Yan
  • Received : 2012.12.10
  • Published : 2013.07.31

Abstract

In this note, we show that $\mathcal{M}({\Gamma}_0(N))$ is a weighted polynomial ring if and only if N = 1, 2, 4, where $\mathcal{M}({\Gamma}_0(N))$ is the graded ring of integral-weighted modular forms for the congruence subgroup ${\Gamma}_0(N)$.

Keywords

modular forms;congruence subgroup;weighted polynomial ring

References

  1. F. Diamond and J. Shurman, A First Course in Modular Forms, Springer-Verlag, 2005.
  2. L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, 2008.
  3. N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1993.
  4. K. Ono, The web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-sereis, American Mathematical Society, 2004.