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Mod p Hecke operators and congruences between modular forms. (English) Zbl 0508.10018


MSC:

11F33 Congruences for modular and \(p\)-adic modular forms
11F11 Holomorphic modular forms of integral weight
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References:

[1] Deligne, P., Rapoport, M.: Schémas de modules de courbes elliptiques, Lecture Notes in Math., vol. 349, pp. 143-174. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0281.14010
[2] Doi, K., Hida, H.: On a certain congruence of cusp forms and the special values of their Dirichlet series. Unpublished manuscript, 1979
[3] Doi, K., Ohta, M.: On some congruences between cusp forms on ?0(N). Lecture Notes in Math., vol. 601, pp. 91-105. Berlin-Heidelberg-New York: 1977 · Zbl 0361.10023
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[9] Jochnowitz, N.: A study of the local components of the Hecke algebra modl. Trans. AMS.270, 253-267 (1982) · Zbl 0536.10021
[10] Koike, M.: A note on modular forms modp. Proc. Japan Acad. Ser. A55, 313-315 (1979) · Zbl 0439.10017 · doi:10.3792/pjaa.55.313
[11] Lang, S.: Introduction to Modular Forms. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0344.10011
[12] Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47, 33-186 (1977) · Zbl 0394.14008
[13] Mazur, B.: Rational isogenies of prime degree. Invent. Math.44, 129-162 (1978) · Zbl 0386.14009 · doi:10.1007/BF01390348
[14] Ribet, K.: Congruences between modular forms on ?0(p q). Proceedings ICM 1983. In preparation · Zbl 0508.10018
[15] Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions, Princeton: Princeton University Press 1971 · Zbl 0221.10029
[16] Wiles, A.: Modular curves and the class group ofQ(? p ). Invent. Math.58, 1-35 (1980) · Zbl 0436.12004 · doi:10.1007/BF01402272
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