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

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References

  1. Borevich, Z.I., Shafarevich, I.R.: Number theory. New York: Academic Press 1966

    Google Scholar 

  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. Carlitz, L., Olson, F.R.: Maillet's determinant. Proc. A.M.S.6, 265–269 (1955)

    Google Scholar 

  4. Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Interscience 1962

    Google Scholar 

  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 1973

    Google Scholar 

  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. Greenberg, R.: A generalization of Kummer's criterion. Inventiones math.21, 247–254 (1973)

    Google Scholar 

  8. Herbrand, J.: Sur les classes des corps circulaires. J. Math. Pures et Appliquées, 9e série11, 417–441 (1932)

    Google Scholar 

  9. Koike, M.: On the congruences between Eisenstein series and cusp forms. US-Japan Number Theory Seminar; Ann Arbor, 1975, Photo-offset notes.

  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, 1976

  11. Leopoldt, H.-W.: Eine Verallgemeinerung der Bernoullischen Zahlen. Abh. Math. Sem. Hamburg22, 131–140 (1958)

    Google Scholar 

  12. Li, W.-C.: Newforms and functional equations. Math. Ann.212, 285–315 (1975)

    Google Scholar 

  13. Masley, J.M., Montgomery, H.L.: Cyclotomic fields with unique factorization. Preprint.

  14. Mazur, B.: Modular curves and the Eisenstein ideal. In preparation.

  15. Raynaud, M.: Schémas en groupes de type (p, ...,p). Bull. Soc. Math. France102, 241–280 (1974)

    Google Scholar 

  16. Serre, J-P: Une interpretation des congruences relatives à la fonction τ de Ramanujan. Sém. Delange-Pisot-Poitou 1967–68, ex. 14

  17. Serre, J-P: Abelianl-adic representations and elliptic curves. New York: Benjamin 1968

    Google Scholar 

  18. Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, no 11, Tokyo-Princeton 1971

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

    Google Scholar 

  20. Tate, J.: Global class field theory. In: Algebraic number theory. Washington: Thompson 1967

    Google Scholar 

  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 

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  1. Fine Hall, 08540, Princeton, N.J., USA

    Kenneth A. Ribet (Sloan Fellow, and visitor at I.H.E.S.)

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  1. Kenneth A. Ribet
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Ribet, K.A. A modular construction of unramifiedp-extensions ofQ(μ p ). Invent Math 34, 151–162 (1976). https://doi.org/10.1007/BF01403065

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