Theta correspondence and Hecke operators relative to a quadratic extension

Ze-Li Dou

Acta Arithmetica (2000)

  • Volume: 93, Issue: 3, page 237-255
  • ISSN: 0065-1036

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Ze-Li Dou. "Theta correspondence and Hecke operators relative to a quadratic extension." Acta Arithmetica 93.3 (2000): 237-255. <http://eudml.org/doc/207413>.

@article{Ze2000,
author = {Ze-Li Dou},
journal = {Acta Arithmetica},
keywords = {Hilbert modular forms; quaternionic automorphic forms; theta functions; theta correspondence; Hecke operators; action of Hecke operators; lifting; modular forms},
language = {eng},
number = {3},
pages = {237-255},
title = {Theta correspondence and Hecke operators relative to a quadratic extension},
url = {http://eudml.org/doc/207413},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Ze-Li Dou
TI - Theta correspondence and Hecke operators relative to a quadratic extension
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 3
SP - 237
EP - 255
LA - eng
KW - Hilbert modular forms; quaternionic automorphic forms; theta functions; theta correspondence; Hecke operators; action of Hecke operators; lifting; modular forms
UR - http://eudml.org/doc/207413
ER -

References

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  1. [D94] Z. L. Dou, On the fundamental periods of Hilbert modular forms, Trans. Amer. Math. Soc. 346 (1994), 147-158. Zbl0822.11044
  2. [D98] Z. L. Dou, On adelic automorphic forms with respect to a quadratic extension, Bull. Austral. Math. Soc., to appear. Zbl0970.11018
  3. [D99] Z. L. Dou, On a theta correspondence with respect to a quadratic extension, J. Number Theory 79 (1999), 1-18. Zbl0943.11025
  4. [Sh80] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. 111 (1980), 313-375. Zbl0438.12003
  5. [Sh81I] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, I, ibid. 114 (1981), 127-164. Zbl0468.10016
  6. [Sh81II] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, II, ibid. 114 (1981), 569-607. Zbl0486.10021
  7. [Sh82] G. Shimura, The periods of certain automorphic forms of arithmetic type, J. Fac. Sci. Univ. Tokyo Sect. IA 28 (1982), 605-632. Zbl0499.10027
  8. [Sh88] G. Shimura, On the critical values of certain Dirichlet series and the periods of automorphic forms, Invent. Math. 94 (1988), 245-305. Zbl0656.10018
  9. [Sh90] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, ibid. 102 (1990), 399-428. Zbl0712.11028
  10. [Sh91] G. Shimura, The critical values of certain Dirichlet series attached to Hilbert modular forms, Duke Math. J. 63 (1991), 557-613. Zbl0752.11021
  11. [Sh93] G. Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), 1011-1052. Zbl0802.11016
  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. Zbl0841.11024

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