Congruences of cusp forms and special values of their zeta functions

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. Atkin, A.O.L., Lehner, J.: Hecke operators on Γ₀(m), Math. Ann.185, 134–160 (1970)

   Google Scholar 

3. Bourbaki, N.: Algebra 9 (sesquilinear forms and quadratic forms), Paris: Hermann 1959

   Google Scholar 

4. Bourbaki, N.: Commutative algebra, Paris: Hermann 1972

   Google Scholar 

5. Bredon, G.E.: Sheaf theory. New York: McGraw-Hill 1967

   Google Scholar 

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. Deligne, P.: Formes modulaires et representationsl-adiques, Sém. Bourbaki, exp. 355, fév. 1969

8. Deligne, P., Serre, J-P.: Formes modulaires de poids 1, Ann. Sci. École Norm. Sup. 4^e série, tome7, 507–530 (1974)

   Google Scholar 

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 Doi, K., Hida, H.: On a certain congruence of cusp forms and the special values of their Dirichlet series, unpublished (1979)

10. Doi, K., Miyake, T.: Automorphic forms and number theory (in Japanese). Tokyo: Kinokuniya Shoten 1976

    Google Scholar 

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 1977

    Google Scholar 

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

    Google Scholar 

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. Hurwitz, A.: Über die Entwicklungskoeffizienten der lemniskatishen Funktionen. Math. Ann.51, 196–226 (1899), (Werke II, 342–373)

    Google Scholar 

15. Labesse, J.-P., Langlands, R.P.:L-indistinguishability forSL(2). Can. J. Math.31, 726–785 (1979)

    Google Scholar 

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 1973

    Google Scholar 

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

    Google Scholar 

19. Mazur, B.: On the arithmetic of special values ofL-functions. Inventiones Math.55, 207–240 (1979)

    Google Scholar 

20. Mazur, B., Swinnerton-Dyer, P.: Arithmetic of Weil curves. Inventiones Math.25, 1–61 (1974)

    Google Scholar 

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

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

    Google Scholar 

23. Ohta, M.: Onl-adic representations attached to automorphic forms, preprint

24. Serre, J-P.: Cohomologie des groupes discrets. In: Prospects in Mathematics. Annals of Mathematics Studies, 70, pp. 77–170, Princeton University Press 1971

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

    Google Scholar 

26. Shimura, G.: Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton University Press 1971

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. Shimura, G.: On the factors of the jacobian variety of a modular function field. J. Math. Soc. Japan25, 523–544 (1973)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

34. [SGA 4III], Théorie des Topos et Cohomologie Etale des Schémas, Tome 3. Lecture Notes in Mathematics, 305. Berlin-Heidelberg-New York: Springer 1973

Download references