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On  -congruences
Author(s):
P.
Guerzhoy
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2743-2746.
MSC (2000):
Primary 11F33
Posted:
May 8, 2007
MathSciNet review:
2317947
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Abstract:
The phenomenon of  -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:
-
- 1.
- Ahlgren, Scott; Ono, Ken, Arithmetic of singular moduli and class polynomials, Compos. Math. 141 (2005), no. 2, 293-312.MR 2134268 (2006a:11058)
- 2.
- 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)
- 3.
- Lang, Serge, Introduction to modular forms, Grundlehren der mathematischen Wissenschaften, No. 222, Springer-Verlag, Berlin-New York, 1976. MR 0429740 (55:2751)
- 4.
- Ono, Ken, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and
 -series, CBMS Reg. Conf. Ser. Math., 102, Amer. Math. Soc., Providence, RI, 2004.MR 2020489 (2005c:11053) - 5.
- Serre, Jean-Pierre, Formes modulaires et fonctions zêta
 -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) - 6.
- Serre, Jean-Pierre, Divisibilité de certaines fonctions arithmétiques, Enseignement Math. (2) 22 (1976), no. 3-4, 227-260. MR 0434996 (55:7958)
- 7.
- Swinnerton-Dyer, H. P. F., On
 -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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