Generalization of Atkin’s orthogonal polynomials and supersingular elliptic curves
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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In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod $p$ for a prime $p$, one gets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.References
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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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3008861