# Theta correspondence and Hecke operators relative to a quadratic extension

Acta Arithmetica (2000)

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

## Access Full Article

top## How to cite

topZe-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

top- [D94] Z. L. Dou, On the fundamental periods of Hilbert modular forms, Trans. Amer. Math. Soc. 346 (1994), 147-158. Zbl0822.11044
- [D98] Z. L. Dou, On adelic automorphic forms with respect to a quadratic extension, Bull. Austral. Math. Soc., to appear. Zbl0970.11018
- [D99] Z. L. Dou, On a theta correspondence with respect to a quadratic extension, J. Number Theory 79 (1999), 1-18. Zbl0943.11025
- [Sh80] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. 111 (1980), 313-375. Zbl0438.12003
- [Sh81I] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, I, ibid. 114 (1981), 127-164. Zbl0468.10016
- [Sh81II] G. Shimura, On certain zeta functions attached to two Hilbert modular forms, II, ibid. 114 (1981), 569-607. Zbl0486.10021
- [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
- [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
- [Sh90] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, ibid. 102 (1990), 399-428. Zbl0712.11028
- [Sh91] G. Shimura, The critical values of certain Dirichlet series attached to Hilbert modular forms, Duke Math. J. 63 (1991), 557-613. Zbl0752.11021
- [Sh93] G. Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), 1011-1052. Zbl0802.11016
- [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. Zbl0841.11024

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.