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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Theta functions of indefinite quadratic forms over real number fields


Author: Olav K. Richter
Journal: Proc. Amer. Math. Soc. 128 (2000), 701-708
MSC (1991): Primary 11F41; Secondary 11F27
Published electronically: September 27, 1999
MathSciNet review: 1706997
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Abstract: We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.


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Additional Information

Olav K. Richter
Affiliation: Department of Mathematics, University of California, San Diego, California 92093-0112
Address at time of publication: Department of Mathematics, University of California, Santa Cruz, California 95064
Email: richter@euclid.ucsd.edu, richter@math.ucsc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05619-1
PII: S 0002-9939(99)05619-1
Received by editor(s): April 29, 1998
Published electronically: September 27, 1999
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1999 American Mathematical Society