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On congruence divisors of cusp forms as factors of the special values of their zeta functions

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References

  1. Bourbaki, N.: Commutative Algebra. Paris: Hermann 1972

    Google Scholar 

  2. Bredon, G.E.: Sheaf Theory. McGraw-Hill 1967

  3. Casselman, W.: On some results of Atkin and Lehner. Math. Ann.201, 301–314 (1973)

    Google Scholar 

  4. Curtis, C.W., Reiner, I.: Representation Theory of Finite Groups and Associative Algebras. Interscience Publishers 1962

  5. Deligne, P.: Formes Modulaires et Representations ℓ-adiques. Sém. Bourbaki, exp. 355, fév. 1969

  6. Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. In: Modular Functions of One Variable, II, Lecture Notes in Mathematics, 349, pp. 143–174. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  7. Doi, K., Hida, H.: On a certain congruence of cusp forms and the special values of their Dirichlet series. unpublished (1979)

  8. Doi, K., Ohta, M.: On some congruences between cusp forms onΓ0(N). In: Modular Functions of One Variable, V, Lecture Notes in Mathematics, 601, pp. 91–105. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  9. Eckmann, B.: Cohomology of groups and transfer. Ann. of Math.58, 481–493 (1953)

    Google Scholar 

  10. Hartshorne, R.: Residues and Duality. Lecture Notes in Mathematics, 20. Berlin Heidelberg New York: Springer 1966

    Google Scholar 

  11. Hida, H.: Congruences of cusp forms and special values of their zeta functions. Invent. Math.63, 225–261 (1981)

    Google Scholar 

  12. Hilton, P.J., Stammbach, U.: A Course in Homological Algebra. Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  13. Katz, N.M.: Higher congruences between modular forms. Ann. of Math.101, 332–367 (1975)

    Google Scholar 

  14. Koike, M.: A note on modular forms modp. Proc. Japan Acad. Ser. A55, 313–315 (1979)

    Google Scholar 

  15. Koizumi, S., Shimura, G.: On specializations of abelian varieties. Sci. Papers. Coll. of Gen. Ed. Univ. of Tokyo9, 187–211 (1959)

    Google Scholar 

  16. Langlands, R.P.: Modular forms and ℓ-adic representation. In: Modular Functions of One Variable, II, Lecture Notes in Mathematics, 349, pp. 361–500. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  17. Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47, 33–186 (1978)

    Google Scholar 

  18. Mazur, B.: Rational isogenies of prime degree. Inventiones Math.44, 129–162 (1978)

    Google Scholar 

  19. Milne, J.S.: Étale Cohomology. Princeton University Press 1980

  20. Miyake, T.: On automorphic forms onGL 2 and Hecke operators. Ann. of Math.94, 174–189 (1971)

    Google Scholar 

  21. Mumford, D.: Abelian Varieties. Tata Institute of Fundamental Research and Oxford University Press 1970

  22. Néron, A.: Modéles minimaux des variétés abéliennes sur les corps locaux et globaux. Publ. Math. I.H.E.S.21, 5–128 (1964)

    Google Scholar 

  23. Ohta, M.: On ℓ-adic representations attached to automorphic forms. Preprint

  24. Serre, J-P.: Sur la topologie des variétés algébriques en caractéristiquep. In: Proc. of Symp. Int. de Top. Alg., pp. 24–53, National University of Mexico 1958

  25. Serre, J-P.: Homologie des groupes. Lecture Notes at Collège de France 1958–1959

  26. Serre, J-P.: Formes modulaires et fonctions zetap-adiques. In: Modular Functions of One Variables, III, Lecture Notes in Mathematics, 350, pp. 191–268. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  27. Serre, J-P., Tate, J.: Good reduction of abelian varieties. Ann. of Math.88, 492–517 (1968)

    Google Scholar 

  28. Shimura, G.: Sur les integrales attachées aux formes automorphes. J. Math. Soc. Japan11, 291–311 (1959)

    Google Scholar 

  29. Shimura, G.: An ℓ-adic method in the theory of automorphic forms. unpublished (1968)

  30. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Iwanami Shoten and Princeton University Press 1971

  31. Shimura, G.: Class fields over real quadratic fields and Hecke operators. Ann. of Math.95, 130–190 (1972)

    Google Scholar 

  32. Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc.31, 79–98 (1975)

    Google Scholar 

  33. Shimura, G.: The special values of the zeta function associated with cusp forms. Comm. Pure Appl. Math.29, 783–804 (1976)

    Google Scholar 

  34. Shimura, G.: On the periods of modular forms. Math. Ann.229, 211–221 (1977)

    Google Scholar 

  35. Shimura, G., Taniyama, Y.: Complex multiplication of abelian varieties and its application to number theory. Publ. Math. Soc. Japan, no. 6, 1961

  36. Sturm, J.: Special values of zeta functions, and Eisenstein series of half integral weight. Amer. J. Math.102, 219–240 (1980)

    Google Scholar 

  37. Swinnerton-Dyer H.P.F.: On ℓ-adic representations and congruences for coefficients of modular forms. In: Modular Functions of One Variables, III, Lecture Notes in Mathematics, 350, pp. 1–55. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  38. Weyl, H.: Classical Groups. Princeton University Press 1939

  39. Wiles, A.: Modular curves and the class group ofQ(ζ p ). Invent. Math.58, 1–35 (1980)

    Google Scholar 

  40. [SGA 4 III], Théorie des Topos et Cohomologie Étale des Schémas. Lectures Notes in Mathematics, 305. Berlin Heidelberg New York: Springer 1973

  41. [SGA 41/2], Cohomologie Étale. Lecture Notes in Mathematics, 569. Berlin Heidelberg New York: Springer 1977

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Author notes

  1. Haruzo Hida

    Present address: Department of Mathematics, Hokkaido University, 060, Sapporo, Japan

Authors and Affiliations

  1. Institute for Advanced Study, School of Mathematics, 08540, Princeton, NJ, USA

    Haruzo Hida

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  1. Haruzo Hida
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Supported in part by National Science Foundation Grant MCS 77-18723 A03

After July, 1981

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Hida, H. On congruence divisors of cusp forms as factors of the special values of their zeta functions. Invent Math 64, 221–262 (1981). https://doi.org/10.1007/BF01389169

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  • DOI: https://doi.org/10.1007/BF01389169

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