## 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

### Citations:

Zbl 0221.10029; Zbl 0459.10018
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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 Unpublished manuscript, 1979 [3] Doi, K., Ohta, M.: On some congruences between cusp forms on ?0(N).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 [4] Hatada, K.: Eigenvalues of Hecke operators onSL(2,Z). Math. Ann.239, 75-96 (1979) · Zbl 0383.10016 [5] Hatada, K.: Congruences for eigenvalues of Hecke operators onSL 2 (Z). Manuscripta Math.34, 305-326 (1981) · Zbl 0462.10017 [6] Hida, H.: Congruences for cusp forms and special values of their zeta functions. Invent. Math.63, 225-261 (1981) · Zbl 0459.10018 [7] Hida, H.: On congruence divisors of cusp forms as factors of the special values of their zeta functions. Invent. Math.64, 221-262 (1981) · Zbl 0472.10028 [8] Hida, H.: Kummer’s criterion for the special values of HeckeL-functions of imaginary quadratic fields and congruences among cusp forms. Invent. Math.66, 415-459 (1982) · Zbl 0485.10019 [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 [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 [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
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