Inventiones mathematicae

, Volume 63, Issue 2, pp 225–261

Congruences of cusp forms and special values of their zeta functions

  • Haruzo Hida


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  1. 1.
    Asai, T.: On the Fourier coefficients of automorphic forms at various cusps and some application to Rankin's convolution, J. Math. Soc. Japan28, 48–61 (1976)Google Scholar
  2. 2.
    Atkin, A.O.L., Lehner, J.: Hecke operators on Γ0(m), Math. Ann.185, 134–160 (1970)Google Scholar
  3. 3.
    Bourbaki, N.: Algebra 9 (sesquilinear forms and quadratic forms), Paris: Hermann 1959Google Scholar
  4. 4.
    Bourbaki, N.: Commutative algebra, Paris: Hermann 1972Google Scholar
  5. 5.
    Bredon, G.E.: Sheaf theory. New York: McGraw-Hill 1967Google Scholar
  6. 6.
    Damerell, R.M.:L-functions of elliptic curves with complex multiplication I, II, Acta Arith.17, 287–301 (1970);19, 311–317 (1971)Google Scholar
  7. 7.
    Deligne, P.: Formes modulaires et representationsl-adiques, Sém. Bourbaki, exp. 355, fév. 1969Google Scholar
  8. 8.
    Deligne, P., Serre, J-P.: Formes modulaires de poids 1, Ann. Sci. École Norm. Sup. 4e série, tome7, 507–530 (1974)Google Scholar
  9. 9.
    Doi, K., Hida, H.: On a certain congruence of cusp forms and the special values of their Dirichlet series, unpublished (1979)Google Scholar
  10. 10.
    Doi, K., Miyake, T.: Automorphic forms and number theory (in Japanese). Tokyo: Kinokuniya Shoten 1976Google Scholar
  11. 11.
    Doi, K., Ohta, M.: On some congruences between cusp forms on Γ0(N). In: Modular functions of one variable, V, Lectures Notes in Mathematics, 601, pp. 91–105. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  12. 12.
    Eckmann, B.: Cohomology of groups and transfer, Ann. of Math.58, 481–493 (1953)Google Scholar
  13. 13.
    Hida, H.: On abelian varieties with complex multiplication as factors of the abelian variety attached to Hilbert modular forms. Jap. J. Math.5, 157–208 (1979)Google Scholar
  14. 14.
    Hurwitz, A.: Über die Entwicklungskoeffizienten der lemniskatishen Funktionen. Math. Ann.51, 196–226 (1899), (Werke II, 342–373)Google Scholar
  15. 15.
    Labesse, J.-P., Langlands, R.P.:L-indistinguishability forSL(2). Can. J. Math.31, 726–785 (1979)Google Scholar
  16. 16.
    Langlands, R.P.: Modular forms andl-adic representations. In: Modular functions of one variable, II, Lecture Notes in Mathematics, 349, pp. 361–500. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  17. 17.
    Matter, K.: Die den Bernoullischen Zahlen analogen Zahlen im Körper der dritten Einheitenwurzeln, Vierteljahrsschrift d. Naturf. Ges. Zürich45, 238–269 (1900)Google Scholar
  18. 18.
    Mazur, B.: Rational isogenies of prime degree. Inventiones Math.44, 129–162 (1978)Google Scholar
  19. 19.
    Mazur, B.: On the arithmetic of special values ofL-functions. Inventiones Math.55, 207–240 (1979)Google Scholar
  20. 20.
    Mazur, B., Swinnerton-Dyer, P.: Arithmetic of Weil curves. Inventiones Math.25, 1–61 (1974)Google Scholar
  21. 21.
    Milne, J.S.: Étale Cohomology, Princeton University Press 1980Google Scholar
  22. 22.
    Miyake, T.: On automorphic forms onGL 2 and Hecke operators. Ann. of Math.94, 174–189 (1971)Google Scholar
  23. 23.
    Ohta, M.: Onl-adic representations attached to automorphic forms, preprintGoogle Scholar
  24. 24.
    Serre, J-P.: Cohomologie des groupes discrets. In: Prospects in Mathematics. Annals of Mathematics Studies, 70, pp. 77–170, Princeton University Press 1971Google Scholar
  25. 25.
    Shimura, G.: Sur les intégrales attachées aux formes automorphes. J. Math. Soc. Japan11, 291–311 (1959)Google Scholar
  26. 26.
    Shimura, G.: Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton University Press 1971Google Scholar
  27. 27.
    Shimura, G.: On elliptic curves with complex multiplication as factors of the jacobians of modular function fields. Nagoya Math. J.43, 199–208 (1971)Google Scholar
  28. 28.
    Shimura, G.: On the factors of the jacobian variety of a modular function field. J. Math. Soc. Japan25, 523–544 (1973)Google Scholar
  29. 29.
    Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc.31, 79–98 (1975)Google Scholar
  30. 30.
    Shimura, G.: The special values of the zeta functions associated with cusp forms. Comm. pure appl. Math.29, 783–804 (1976)Google Scholar
  31. 31.
    Shimura, G.: On the periods of modular forms. Math. Ann.229, 211–221 (1977)Google Scholar
  32. 32.
    Shimura, G.: The special values of the zeta functions associated with Hilbert modular forms. Duke Math. J.45, 637–679 (1978)Google Scholar
  33. 33.
    Sturm, J.: Special values of zeta functions and Eisenstein series of half integral weight. Amer. J.102, 219–240 (1980)Google Scholar
  34. 34.
    [SGA 4III], Théorie des Topos et Cohomologie Etale des Schémas, Tome 3. Lecture Notes in Mathematics, 305. Berlin-Heidelberg-New York: Springer 1973Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Haruzo Hida
    • 1
    • 2
  1. 1.Hokkaido UniversitySapporoJapan
  2. 2.The Institute for Advanced StudyPrincetonUSA

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