A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\). (English) Zbl 0338.12003


11R23 Iwasawa theory
11F03 Modular and automorphic functions
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
14L15 Group schemes
11R18 Cyclotomic extensions
Full Text: DOI EuDML


[1] Borevich, Z.I., Shafarevich, I.R.: Number theory. New York: Academic Press 1966 · Zbl 0145.04902
[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) · Zbl 0131.03602
[3] Carlitz, L., Olson, F.R.: Maillet’s determinant. Proc. A.M.S.6, 265-269 (1955) · Zbl 0065.02703
[4] Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Interscience 1962 · Zbl 0131.25601
[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
[6] Deligne, P., Serre, J-P.: Formes modulaires de poids 1. Ann. Scient. Ec. Norm. Sup., 4e série,7, 507-530 (1974) · Zbl 0321.10026
[7] Greenberg, R.: A generalization of Kummer’s criterion. Inventiones math.21, 247-254 (1973) · Zbl 0269.12005
[8] Herbrand, J.: Sur les classes des corps circulaires. J. Math. Pures et Appliquées, 9e série11, 417-441 (1932) · JFM 58.0180.02
[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) · Zbl 0080.03002
[12] Li, W.-C.: Newforms and functional equations. Math. Ann.212, 285-315 (1975) · Zbl 0286.10016
[13] Masley, J.M., Montgomery, H.L.: Cyclotomic fields with unique factorization. Preprint. · Zbl 0335.12013
[14] Mazur, B.: Modular curves and the Eisenstein ideal. In preparation. · Zbl 0394.14008
[15] Raynaud, M.: Schémas en groupes de type (p, ...,p). Bull. Soc. Math. France102, 241-280 (1974) · Zbl 0325.14020
[16] Serre, J-P: Une interpretation des congruences relatives à la fonction ? de Ramanujan. Sém. Delange-Pisot-Poitou 1967-68, ex. 14
[17] Serre, J-P: Abelianl-adic representations and elliptic curves. New York: Benjamin 1968
[18] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, no 11, Tokyo-Princeton 1971 · Zbl 0221.10029
[19] Shimura, G.: Class fields over real quadratic fields and Hecke operators. Ann. of Math.95, 130-190 (1972) · Zbl 0255.10032
[20] Tate, J.: Global class field theory. In: Algebraic number theory. Washington: Thompson 1967 · Zbl 1179.11041
[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) · Zbl 0287.14011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.