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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generalization of Atkin’s orthogonal polynomials and supersingular elliptic curves
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by Ying-Ying Tran PDF
Proc. Amer. Math. Soc. 141 (2013), 1135-1141 Request permission

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In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod $p$ for a prime $p$, one gets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
  • George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999. MR 1688958, DOI 10.1017/CBO9781107325937
  • M. Kaneko and D. Zagier, Supersingular $j$-invariants, hypergeometric series, and Atkin’s orthogonal polynomials, Computational perspectives on number theory (Chicago, IL, 1995) AMS/IP Stud. Adv. Math., vol. 7, Amer. Math. Soc., Providence, RI, 1998, pp. 97–126. MR 1486833, DOI 10.1090/amsip/007/05
  • Ken Ono, The web of modularity: arithmetic of the coefficients of modular forms and $q$-series, CBMS Regional Conference Series in Mathematics, vol. 102, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004. MR 2020489
  • Jean-Pierre Serre, Congruences et formes modulaires [d’après H. P. F. Swinnerton-Dyer], Séminaire Bourbaki, 24e année (1971/1972), Exp. No. 416, Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973, pp. 319–338 (French). MR 0466020
  • Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8
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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