충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제29권3호
  • /
  • Pages.509-514
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  • 2016
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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STUDY ON THE ARITHMETIC OF MODULAR FORMS

  • Choi, SoYoung (Department of Mathematics Education and RINS Gyeongsang National University)
  • 투고 : 2016.07.06
  • 심사 : 2016.07.29
  • 발행 : 2016.08.15
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초록

By constructing a canonical basis for the space $M_k^{\sharp}({\Gamma}_0(N))$ explicitly, we find a basis of the space of cusp forms for ${\Gamma}_0(N)$ consisting of $Poincar{\acute{e}}$ series.

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참고문헌

  1. J. Ahn and S. Choi, Arithmetic of weakly holomorphic modular forms for Hecke groups, JP Journal of Algebra, Number Theory and Application 37 (2015), no. 2, 105-124. https://doi.org/10.17654/JPANTAOct2015_105_124
  2. J. H. Bruinier, K. Ono, R. C. Rhoades, and C. Robert, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Math. Ann. 342 (2008), no. 3, 673-693. https://doi.org/10.1007/s00208-008-0252-1
  3. D. Choi, Spaces of modular forms generated by eta-quotients, Ramanujan J. 14 (2007), no. 1, 69-77. https://doi.org/10.1007/s11139-006-9007-3
  4. H. Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997.
  5. T. Miyake, Modular forms, Springer, 1989
  6. C. R. Rhoades, Linear relations among Poincare series via harmonic weak Maass forms, Ramanujan J. 29 (2012), no. 1-3, 311-320. https://doi.org/10.1007/s11139-012-9377-7