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On $ U(p)$-congruences

Author(s): P. Guerzhoy
Journal: Proc. Amer. Math. Soc. 135 (2007), 2743-2746.
MSC (2000): Primary 11F33
Posted: May 8, 2007
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Abstract: The phenomenon of $ U(p)$-congruences was recently studied by Ahlgren and Ono (2005) and by Elkies, Ono and Yang (2005). We provide a necessary and sufficient condition which improves their general results.

References:

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Ahlgren, Scott; Ono, Ken, Arithmetic of singular moduli and class polynomials, Compos. Math. 141 (2005), no. 2, 293-312.MR 2134268 (2006a:11058)

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Elkies, Noam; Ono, Ken; Yang, Tonghai, Reduction of CM elliptic curves and modular function congruences, Int. Math. Res. Not. (2005), no. 44, 2695-2707.MR 2181309 (2006k:11076)

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Lang, Serge, Introduction to modular forms, Grundlehren der mathematischen Wissenschaften, No. 222, Springer-Verlag, Berlin-New York, 1976. MR 0429740 (55:2751)

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Ono, Ken, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $ q$-series, CBMS Reg. Conf. Ser. Math., 102, Amer. Math. Soc., Providence, RI, 2004.MR 2020489 (2005c:11053)

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Serre, Jean-Pierre, Formes modulaires et fonctions zêta $ p$-adiques, Modular functions of one variable, III, Proc. Internat. Summer School, Univ. Antwerp, 1972, pp. 191-268, Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973.MR 0404145 (53:7949a)

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Swinnerton-Dyer, H. P. F., On $ l$-adic representations and congruences for coefficients of modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, 1972), pp. 1-55, Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973. MR 0406931 (53:10717a)

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Additional Information:

P. Guerzhoy
Affiliation: Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822-2273
Email: p.guerzhoy@gmail.com

DOI: 10.1090/S0002-9939-07-08816-8
PII: S 0002-9939(07)08816-8
Received by editor(s): May 2, 2006
Received by editor(s) in revised form: June 6, 2006
Posted: May 8, 2007
Additional Notes: The research of this author was supported by NSF grant DMS-0501225
Communicated by: Ken Ono
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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