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ArticleOriginal scientific text

Title

Theta correspondence and Hecke operators relative to a quadratic extension

Authors 1

Affiliations

  1. Mathematics Department, P.O. Box 298900, Texas Christian University, Fort Worth, TX 76129, U.S.A.

Keywords

ENG
Hilbert modular forms, quaternionic automorphic forms, theta functions, theta correspondence, Hecke operators

Bibliography

  1. [D94] Z. L. Dou, On the fundamental periods of Hilbert modular forms, Trans. Amer. Math. Soc. 346 (1994), 147-158.
  2. [D98] Z. L. Dou, On adelic automorphic forms with respect to a quadratic extension, Bull. Austral. Math. Soc., to appear.
  3. [D99] Z. L. Dou, On a theta correspondence with respect to a quadratic extension, J. Number Theory 79 (1999), 1-18.
  4. [Sh80] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. 111 (1980), 313-375.
  5. [Sh81I] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, I, ibid. 114 (1981), 127-164.
  6. [Sh81II] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, II, ibid. 114 (1981), 569-607.
  7. [Sh82] G. Shimura, The periods of certain automorphic forms of arithmetic type, J. Fac. Sci. Univ. Tokyo Sect. IA 28 (1982), 605-632.
  8. [Sh88] G. Shimura, On the critical values of certain Dirichlet series and the periods of automorphic forms, Invent. Math. 94 (1988), 245-305.
  9. [Sh90] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, ibid. 102 (1990), 399-428.
  10. [Sh91] G. Shimura, The critical values of certain Dirichlet series attached to Hilbert modular forms, Duke Math. J. 63 (1991), 557-613.
  11. [Sh93] G. Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), 1011-1052.
  12. [Sh] G. Shimura, Two correspondences to Ze-Li Dou, unpublished.
  13. [Y] H. Yoshida, On a conjecture of Shimura concerning periods of Hilbert modular forms, Amer. J. Math. 117 (1995), 1019-1038.
Acta Arithmetica
2000/93/3
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Pages:
237-255
Main language of publication
English
Received
1998-11-02
Accepted
1999-06-15
Published
2000
Exact and natural sciences