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Generalization of Atkin's orthogonal polynomials and supersingular elliptic curves


Author: Ying-Ying Tran
Journal: Proc. Amer. Math. Soc. 141 (2013), 1135-1141
MSC (2010): Primary 14H52, 11F33
DOI: https://doi.org/10.1090/S0002-9939-2012-11433-9
Published electronically: August 20, 2012
MathSciNet review: 3008861
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Abstract: In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod $ p$ for a prime $ p$, one gets the locus of supersingular elliptic curves. Here we generalize this phenomenon by considering the continued fraction expansions of modular and quasimodular forms.


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Additional Information

Ying-Ying Tran
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
Email: yytran@math.cornell.edu

DOI: https://doi.org/10.1090/S0002-9939-2012-11433-9
Received by editor(s): July 22, 2010
Received by editor(s) in revised form: August 9, 2011
Published electronically: August 20, 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.