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

 

On the independence of Heegner points on CM elliptic curves associated to distinct quadratic imaginary fields


Author: Hatice Şahinoğlu
Journal: Proc. Amer. Math. Soc. 141 (2013), 813-826
MSC (2010): Primary 11G05; Secondary 11R37, 14H25
Published electronically: July 19, 2012
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Abstract: In this paper we give a sufficient condition on the class numbers of distinct quadratic imaginary fields so that on a given CM elliptic curve over $ \mathbb{Q}$ with fixed modular parameterization, the Heegner points associated to (the maximal orders of) these quadratic imaginary fields are linearly independent. This extends results of Rosen and Silverman from the non-CM to the CM case.


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Additional Information

Hatice Şahinoğlu
Affiliation: Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, Rhode Island 02912

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11389-9
PII: S 0002-9939(2012)11389-9
Keywords: Elliptic curve, Heegner points
Received by editor(s): March 9, 2011
Received by editor(s) in revised form: March 10, 2011, June 27, 2011, and July 22, 2011
Published electronically: July 19, 2012
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.