Advertisement

Inventiones mathematicae

, Volume 34, Issue 3, pp 151–162 | Cite as

A modular construction of unramifiedp-extensions ofQ(μ p )

  • Kenneth A. Ribet
Article

Keywords

Modular Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Borevich, Z.I., Shafarevich, I.R.: Number theory. New York: Academic Press 1966Google Scholar
  2. 2.
    Carlitz, L.: A generalization of Maillet's determinant and a bound for the first factor of the class number. Proc. A.M.S.12, 256–261 (1961)Google Scholar
  3. 3.
    Carlitz, L., Olson, F.R.: Maillet's determinant. Proc. A.M.S.6, 265–269 (1955)Google Scholar
  4. 4.
    Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Interscience 1962Google Scholar
  5. 5.
    Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. International Summer School on Modular Functions; Antwerp, 1972. Lecture Notes in Math.349, pp. 143–316. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  6. 6.
    Deligne, P., Serre, J-P.: Formes modulaires de poids 1. Ann. Scient. Ec. Norm. Sup., 4e série,7, 507–530 (1974)Google Scholar
  7. 7.
    Greenberg, R.: A generalization of Kummer's criterion. Inventiones math.21, 247–254 (1973)Google Scholar
  8. 8.
    Herbrand, J.: Sur les classes des corps circulaires. J. Math. Pures et Appliquées, 9e série11, 417–441 (1932)Google Scholar
  9. 9.
    Koike, M.: On the congruences between Eisenstein series and cusp forms. US-Japan Number Theory Seminar; Ann Arbor, 1975, Photo-offset notes.Google Scholar
  10. 10.
    Koike, M.: Congruences between cusp forms of weight one and weight two and a remark on a theorem of Deligne and Serre. International Symposium on Algebraic Number Theory; Kyoto, 1976Google Scholar
  11. 11.
    Leopoldt, H.-W.: Eine Verallgemeinerung der Bernoullischen Zahlen. Abh. Math. Sem. Hamburg22, 131–140 (1958)Google Scholar
  12. 12.
    Li, W.-C.: Newforms and functional equations. Math. Ann.212, 285–315 (1975)Google Scholar
  13. 13.
    Masley, J.M., Montgomery, H.L.: Cyclotomic fields with unique factorization. Preprint.Google Scholar
  14. 14.
    Mazur, B.: Modular curves and the Eisenstein ideal. In preparation.Google Scholar
  15. 15.
    Raynaud, M.: Schémas en groupes de type (p, ...,p). Bull. Soc. Math. France102, 241–280 (1974)Google Scholar
  16. 16.
    Serre, J-P: Une interpretation des congruences relatives à la fonction τ de Ramanujan. Sém. Delange-Pisot-Poitou 1967–68, ex. 14Google Scholar
  17. 17.
    Serre, J-P: Abelianl-adic representations and elliptic curves. New York: Benjamin 1968Google Scholar
  18. 18.
    Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, no 11, Tokyo-Princeton 1971Google Scholar
  19. 19.
    Shimura, G.: Class fields over real quadratic fields and Hecke operators. Ann. of Math.95, 130–190 (1972)Google Scholar
  20. 20.
    Tate, J.: Global class field theory. In: Algebraic number theory. Washington: Thompson 1967Google Scholar
  21. 21.
    Yamauchi, M.: On the fields generated by certain points of finite order on Shimura's elliptic curves. J. Math. Kyoto Univ.14, 243–255 (1974)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Kenneth A. Ribet
    • 1
  1. 1.PrincetonUSA

Personalised recommendations