Heegner zeros of theta functions
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- by Jorge Jimenez-Urroz and Tonghai Yang PDF
- Trans. Amer. Math. Soc. 355 (2003), 4137-4149 Request permission
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 $-7$. This leads to some interesting questions on the arithmetic of certain elliptic curves, which we also address here.References
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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
- MR Author ID: 606823
- Email: thyang@math.wisc.edu
- Received by editor(s): February 25, 2002
- Received by editor(s) in revised form: December 20, 2002
- Published electronically: 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 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4137-4149
- MSC (2000): Primary 11G05, 11M20, 14H52
- DOI: https://doi.org/10.1090/S0002-9947-03-03277-X
- MathSciNet review: 1990579