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On the Stickelberger ideal and the circular units of an abelian field. (English) Zbl 0465.12001

MSC:
11R18 Cyclotomic extensions
11R27 Units and factorization
11R23 Iwasawa theory
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References:
[1] [G] Gillard, R.: Remarques sur les Unités Cyclotomiques et les Unités Elliptiques. J. Number Theory11, 21-48 (1979) · Zbl 0405.12008 · doi:10.1016/0022-314X(79)90018-0
[2] [H] Hasse, H.: Über die Klassenzahl abelscher Zahlkörper. Berlin: Akademie-Verlag 1952 · Zbl 0063.01966
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[4] [K] Kummer, E.E.: Mémoire sur la théorie des nombres complexes composés de racines de l’unité et de nombres entiers. Collected Papers I. Berlin-Heidelberg-New York: Springer-Verlag 1975
[5] [L] Leopoldt, H.W.: Über Einheitengruppe und Klassenzahl reeller abelscher Zahlkörper. Abh. Deutsche Akad. Wiss. Berlin, math.-nat. Klasse 1953, No. 2 (1954)
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[7] [Sch] Schmidt C.-G.: Größencharaktere und Relativklassenzahl abelscher Zahlkörper. J. Number Theory11, 128-159 (1979) · Zbl 0403.12009 · doi:10.1016/0022-314X(79)90026-X
[8] [S] Sinnott, W.: On the Stickelberger ideal and the circular units of a cyclotomic field. Ann. of Math.108, 107-134 (1978) · Zbl 0395.12014 · doi:10.2307/1970932
[9] [W] Weil, A.: Sommes de Jacobi et caractères de Hecke, Nachrichten der Akad. Göttingen 1-14, 1974 · Zbl 0367.10035
[10] [WW] Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Cambridge Univ. Press, 1962
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