A note on Sinnott's index formula

Kazuhiro Dohmae

Acta Arithmetica (1997)

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

Abstract

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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].

How to cite

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Kazuhiro 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

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  1. [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. [2] R. Gold and J. Kim, Bases for cyclotomic units, Compositio Math. 71 (1989), 13-28. Zbl0687.12003
  3. [3] R. Kučera, On bases of odd and even universal ordinary distributions, J. Number Theory 40 (1992), 264-283. Zbl0744.11051
  4. [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. [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. [6] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
  7. [7] L. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, New York, 1980. 

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