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ISSN 1088-6826(e) ISSN 0002-9939(p)

On ordinary primes for modular forms and the theta operator

Author(s): Masataka Chida; Masanobu Kaneko
Journal: Proc. Amer. Math. Soc. 135 (2007), 1001-1005.
MSC (2000): Primary 11F33; Secondary 11F11
Posted: October 13, 2006
MathSciNet review: 2262900
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Abstract | References | Similar articles | Additional information

Abstract: We give a criterion for a prime being ordinary for a modular form, by using the theta operator of Ramanujan.

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N. Jochnowitz, A study of the local components of the Hecke algebra mod , Trans. Amer. Math. Soc. 270 (1982), no. 1, 253-267. MR 0642340 (83e:10033a)

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M. Kaneko, D. Zagier, Supersingular -invariants, hypergeometric series, and Atkin's orthogonal polynomials, Computational perspectives on number theory (Chicago, IL, 1995), 97-126, AMS/IP Stud. Adv. Math., 7. MR 1486833 (99b:11064)

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J.-P. Serre, Congruences et formes modulaires (d'après H. P. F. Swinnerton-Dyer), Séminaire Bourbaki 1971/72, 416

( $\OE$ uvres, vol. 3, 74-88). MR 0466020 (57:5904a)

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H. P. F. Swinnerton-Dyer, On $\ell$ -adic representations and congruences for coefficients of modular forms, Lect. Notes. in Math. 350 (1973), 1-55. MR 0406931 (53:10717a)

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D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 57-75. MR 1280058 (95d:11048)

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Additional Information:

Masataka Chida
Affiliation: Institute of Mathematics, Tohoku University, Aoba, Sendai, 980-8578, Japan
Email: sa2m22@math.tohoku.ac.jp

Masanobu Kaneko
Affiliation: Faculty of Mathematics, Kyushu University 33, Fukuoka, 812-8581, Japan
Email: mkaneko@math.kyushu-u.ac.jp

DOI: 10.1090/S0002-9939-06-08561-3
PII: S 0002-9939(06)08561-3
Keywords: Ordinary prime, theta operator
Received by editor(s): October 13, 2005
Received by editor(s) in revised form: November 15, 2005
Posted: October 13, 2006
Additional Notes: The first author was supported in part by JSPS Research Fellowships for Young Scientists
Communicated by: Ken Ono
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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