Browse > Article
http://dx.doi.org/10.4134/CKMS.2013.28.3.481

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

Kim, Daeyeoul (National Institute for Mathematical Sciences)
Li, Yan (Department of Applied Mathematics China Agriculture University)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 481-486 More about this Journal
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;
Citations & Related Records
연도 인용수 순위
  • Reference
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.