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A note on a lemma of Shimura
Author(s):
Ze-Li
Dou
Journal:
Proc. Amer. Math. Soc.
131
(2003),
77-82.
MSC (2000):
Primary 11F30, 11F41, 11F55, 11F67
Posted:
May 22, 2002
MathSciNet review:
1929025
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Abstract:
The subject of this paper is a quaternion algebra over a quadratic extension of a totally real algebraic number field. We generalize an important technical lemma of Shimura, on which a certain period of automorphic forms depends.
References:
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- [D1]
- Z.-L. Dou, On a theta correspondence with respect to a quadratic extension, J. Number Theory 79 (1999), 1-18. MR 2000j:11063
- [D2]
- -, Theta correspondence and Hecke operators relative to a quadratic extension, Acta Arithmetica XCIII.3 (2000), 237-255. MR 2001f:11074
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- -, On the fundamental periods of Hilbert modular forms, Transactions of the American Mathematical Society 346 (1994), 147-158. MR 95b:11052
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- D. A. Hejhal, A classical approach to a well-known correspondence on quaternion groups, Lecture Notes in Math. 1135 (1985), 127-196, Springer-Verlag. MR 87h:11045
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- G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. Math. 111 (1980), 313-375. MR 81g:10041
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- -, On certain zeta functions attached to two Hilbert modular forms, I, Ann. Math. 114 (1981), 127-164. MR 83d:10036a
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- -, On certain zeta functions attached to two Hilbert modular forms, II, Ann. Math. 114 (1981), 569-607. MR 83d:10036b
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Additional Information:
Ze-Li
Dou
Affiliation:
Department of Mathematics, Texas Christian University, P. O. Box 298900, Fort Worth, Texas 76129
Email:
z.dou@tcu.edu
DOI:
10.1090/S0002-9939-02-06652-2
PII:
S 0002-9939(02)06652-2
Keywords:
Quaternionic automorphic forms,
periods of automorphic forms,
theta correspondence
Received by editor(s):
February 14, 2000
Received by editor(s) in revised form:
August 22, 2001
Posted:
May 22, 2002
Additional Notes:
Research for this article was partially supported by NSA Grant MDA904-97-1-0109 and by the Texas Christian University Research Fund.
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2002,
American Mathematical Society
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