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

 

Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4


Author: Tonghai Yang
Journal: Proc. Amer. Math. Soc. 126 (1998), 999-1004
MSC (1991): Primary 11F27, 11F67, 11M06
MathSciNet review: 1443174
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Abstract: In this note, we apply the method of Rodriguez Villegas and Yang (1996) to construct a family of infinite many theta series over the Hilbert-Blumenthal modular surfaces with a common zero. We also relate the non-vanishing of the central L-values of certain Hecke characters of non-biquadratic CM number fields of degree 4 to the nonvanishing of theta functions at CM points in the Hilbert-Blumenthal modular surfaces.


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Additional Information

Tonghai Yang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: thyang@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04213-0
PII: S 0002-9939(98)04213-0
Keywords: Theta function, central Hecke L-value, ideal class number
Received by editor(s): September 27, 1996
Additional Notes: The author was partially supported by NSF grant DMS-9304580
Communicated by: William W. Adams
Article copyright: © Copyright 1998 American Mathematical Society