Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l

• Autorzy: Stanislav Jakubec
• Języki publikacji: EN

Kategorie tematyczne

• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 4
• Strony: 293-310

Daty

wydano

1996

otrzymano

1994-11-16

poprawiono

1995-07-12

Twórcy

autor

Stanislav Jakubec

• Matematický ústav SAV, Štefánikova 49, 814 73 Bratislava, Slovakia

Bibliografia

• [1] K. Q. Feng, The Ankeny-Artin-Chowla formula for cubic cyclic number fields, J. China Univ. Sci. Tech. 12 (1982), 20-27.
• [2] S. Jakubec, The congruence for Gauss period, J. Number Theory 48 (1994), 36-45.
• [3] S. Jakubec, On divisibility of class number of real Abelian fields of prime conductor, Abh. Math. Sem. Univ. Hamburg 63 (1993), 67-86.
• [4] S. Jakubec, On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg 64 (1994), 105-124.
• [5] S. Jakubec, Congruence of Ankeny-Artin-Chowla type for cyclic fields of prime degree l, Math. Proc. Cambridge Philos. Soc., to appear.
• [6] A. A. Kiselev and I. Sh. Slavutskiĭ, The transformation of Dirichlet's formulas and the arithmetical computation of the class number of quadratic fields, in: Proc. Fourth All-Union Math. Congr. (Leningrad 1961), Vol. II, Nauka, Leningrad, 1964, 105-112 (in Russian).
• [7] F. Marko, On the existence of p-units and Minkowski units in totally real cyclic fields, Abh. Math. Sem. Univ. Hamburg, to appear.
• [8] R. Schertz, Über die analytische Klassenzahlformel für reelle abelsche Zahlkörper, J. Reine Angew. Math. 307/308 (1979), 424-430.
• [9] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234.
• [10] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, in: Séminaire de Théorie des Nombres, Paris 1979-80, M.-J. Bertin (ed.), Progr. Math. 12, Birkhäuser, 1981, 277-286.