Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE REPRESENTABILITY OF MODULAR FORMS BY CERTAIN THETA SERIES

  • Jun, Sung-Tae (Department of Applied Mathematics Kunkuk University)
  • Published : 1997.11.01
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Abstract

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

Keywords

References

  1. Math. ann v.185 Hecke operators of $Γ_0(N)$ A. Atkin;J. Lehner
  2. J. Reine Angew Math v.43 On automorphisms of Quaternion orders J. Brezinski
  3. J. Mat. Zeit. v.43 Uber die Idealklassenzahl total definiter Quaternionen-Algebren M. Eichler
  4. Acta Arith v.4 Quadratische Formen und Modularfunktionen M. Eichler
  5. Lecture Notes in Math v.320 The basis problem for modular forms and the traces of Hecke operators M. Eichler
  6. Math Werke Analytische Arithmetik der positiven quadratischen Formen E. Hecke
  7. J. Math. Soc. Japan. v.26 Explicit formula of the traces of the Hecke operators for $Γ_0(N)$ H. Hijikata
  8. J. Reine angew Math v.394 Orders in Quaternion Algebras H. Hijikata;A. Pizer;T. Shemanske
  9. Memoirs of AMS v.82 The basis problem for modular forms on $Γ_0(N)$ H. Hijikata;A. Pizer;T. Shemanske
  10. preprint On the certain primitive orders S. Jun
  11. Comm. K. M. S. v.10 Theta series by primitive orders S. Jun
  12. The algebraic theroy of Qudratic forms T. Lam
  13. J. Math. Soc. Japan. v.28 On the arithmetic of Quaternion algebras II A. Pizer
  14. Math. Ann. v.226 The action of the Canoical involution on Moular forms of Weight 2 on $Γ_0(N)$ A. Pizer
  15. J. Algebra v.64 An Algorithm for computing modular forms on $Γ_0(N)$ A. Pizer
  16. Maximal Orders I. Reiner
  17. Annals of Math Uber die analytische Theorie der quadratischen Formen C. L. Siegel