대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제28권3호
  • /
  • Pages.481-486
  • /
  • 2013
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2012.12.10
  • 발행 : 2013.07.31
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초록

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 ${\Gamma}_0(N)$.

키워드

참고문헌

  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.