Theta correspondence and Hecke operators relative to a quadratic extension

• Autorzy: Ze-Li Dou
• Języki publikacji: EN

Słowa kluczowe

EN

Hilbert modular forms; quaternionic automorphic forms; theta functions; theta correspondence; Hecke operators

Kategorie tematyczne

• 11F41: Automorphic forms on GL ( 2 ) ; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
• 11F32: Modular correspondences, etc.
• 11F55: Other groups and their modular and automorphic forms (several variables)
• 11F60: Hecke-Petersson operators, differential operators (several variables)
• 11F27: Theta series; Weil representation; theta correspondences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 3
• Strony: 237-255

Daty

wydano

2000

otrzymano

1998-11-02

poprawiono

1999-06-15

Twórcy

autor

Ze-Li Dou

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

Bibliografia

• [D94] Z. L. Dou, On the fundamental periods of Hilbert modular forms, Trans. Amer. Math. Soc. 346 (1994), 147-158.
• [D98] Z. L. Dou, On adelic automorphic forms with respect to a quadratic extension, Bull. Austral. Math. Soc., to appear.
• [D99] Z. L. Dou, On a theta correspondence with respect to a quadratic extension, J. Number Theory 79 (1999), 1-18.
• [Sh80] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. 111 (1980), 313-375.
• [Sh81I] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, I, ibid. 114 (1981), 127-164.
• [Sh81II] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, II, ibid. 114 (1981), 569-607.
• [Sh82] G. Shimura, The periods of certain automorphic forms of arithmetic type, J. Fac. Sci. Univ. Tokyo Sect. IA 28 (1982), 605-632.
• [Sh88] G. Shimura, On the critical values of certain Dirichlet series and the periods of automorphic forms, Invent. Math. 94 (1988), 245-305.
• [Sh90] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, ibid. 102 (1990), 399-428.
• [Sh91] G. Shimura, The critical values of certain Dirichlet series attached to Hilbert modular forms, Duke Math. J. 63 (1991), 557-613.
• [Sh93] G. Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), 1011-1052.
• [Sh] G. Shimura, Two correspondences to Ze-Li Dou, unpublished.
• [Y] H. Yoshida, On a conjecture of Shimura concerning periods of Hilbert modular forms, Amer. J. Math. 117 (1995), 1019-1038.