A note on Sinnott's index formula

• Autorzy: Kazuhiro Dohmae
• Języki publikacji: EN

Abstrakty

EN

Let k be an (imaginary or real) abelian number field whose conductor has two distinct prime divisors. We shall construct a basis for the group C of circular units in k and compute the index of C in the group E of units in k. This result is a generalization of Theorem 3.3 in a previous paper [1].

Kategorie tematyczne

• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 1
• Strony: 57-67

Daty

wydano

1997

otrzymano

1996-09-26

poprawiono

1997-04-07

Twórcy

autor

Kazuhiro Dohmae

• Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-03, Japan

Bibliografia

• [1] K. Dohmae, On bases of groups of circular units of some imaginary abelian number fields, J. Number Theory 61 (1996), 343-364.
• [2] R. Gold and J. Kim, Bases for cyclotomic units, Compositio Math. 71 (1989), 13-28.
• [3] R. Kučera, On bases of odd and even universal ordinary distributions, J. Number Theory 40 (1992), 264-283.
• [4] R. Kučera, On bases of the Stickelberger ideal and of the group of circular units of a cyclotomic field, J. Number Theory., 284-316.
• [5] W. Sinnott, On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. 108 (1978), 107-134.
• [6] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234.
• [7] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, New York, 1980.