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Heegner zeros of theta functions
Author(s):
Jorge
Jimenez-Urroz;
Tonghai
Yang
Journal:
Trans. Amer. Math. Soc.
355
(2003),
4137-4149.
MSC (2000):
Primary 11G05, 11M20, 14H52
Posted:
June 18, 2003
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Abstract:
Heegner divisors play an important role in number theory. However, little is known on whether a modular form has Heegner zeros. In this paper, we start to study this question for a family of classical theta functions, and prove a quantitative result, which roughly says that many of these theta functions have a Heegner zero of discriminant  . This leads to some interesting questions on the arithmetic of certain elliptic curves, which we also address here.
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Additional Information:
Jorge
Jimenez-Urroz
Affiliation:
Departamento de Matemática Aplicada IV, ETSETB, Universidad Politecnica de Catalunya, 08034 Barcelona, España
Email:
jjimenez@mat.upc.es
Tonghai
Yang
Affiliation:
Department of Mathematics, University of Wisconsin Madison, Madison, Wisconsin 53717
Email:
thyang@math.wisc.edu
DOI:
10.1090/S0002-9947-03-03277-X
PII:
S 0002-9947(03)03277-X
Keywords:
Theta functions,
elliptic curves,
Heegner points
Received by editor(s):
February 25, 2002
Received by editor(s) in revised form:
December 20, 2002
Posted:
June 18, 2003
Additional Notes:
The first author was partially supported by PB90-0179 and Ramon y Cajal program of MCYT. The second author was partially supported by NSF grant DMS-0070476
Copyright of article:
Copyright
2003,
American Mathematical Society
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