# A note on Sinnott's index formula

Acta Arithmetica (1997)

- Volume: 82, Issue: 1, page 57-67
- ISSN: 0065-1036

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topKazuhiro Dohmae. "A note on Sinnott's index formula." Acta Arithmetica 82.1 (1997): 57-67. <http://eudml.org/doc/207078>.

@article{KazuhiroDohmae1997,

abstract = {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].},

author = {Kazuhiro Dohmae},

journal = {Acta Arithmetica},

keywords = {circular units; class number; imaginary abelian number field; Sinnott's index formula},

language = {eng},

number = {1},

pages = {57-67},

title = {A note on Sinnott's index formula},

url = {http://eudml.org/doc/207078},

volume = {82},

year = {1997},

}

TY - JOUR

AU - Kazuhiro Dohmae

TI - A note on Sinnott's index formula

JO - Acta Arithmetica

PY - 1997

VL - 82

IS - 1

SP - 57

EP - 67

AB - 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].

LA - eng

KW - circular units; class number; imaginary abelian number field; Sinnott's index formula

UR - http://eudml.org/doc/207078

ER -

## References

top- [1] K. Dohmae, On bases of groups of circular units of some imaginary abelian number fields, J. Number Theory 61 (1996), 343-364. Zbl0869.11082
- [2] R. Gold and J. Kim, Bases for cyclotomic units, Compositio Math. 71 (1989), 13-28. Zbl0687.12003
- [3] R. Kučera, On bases of odd and even universal ordinary distributions, J. Number Theory 40 (1992), 264-283. Zbl0744.11051
- [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. Zbl0744.11052
- [5] W. Sinnott, On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. 108 (1978), 107-134. Zbl0395.12014
- [6] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
- [7] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, New York, 1980.

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