Geodesic
Circular units of real abelian fields with four ramified primes
Archivum mathematicum, Tome 53 (2017) no. 4, pp. 221-252
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we study the groups of circular numbers and circular units in Sinnott’s sense in real abelian fields with exactly four ramified primes under certain conditions. More specifically, we construct $\mathbb{Z}$-bases for them in five special infinite families of cases. We also derive some results about the corresponding module of relations (in one family of cases, we show that the module of Ennola relations is cyclic). The paper is based upon the thesis [6], which builds upon the results of the paper [2].
In this paper we study the groups of circular numbers and circular units in Sinnott’s sense in real abelian fields with exactly four ramified primes under certain conditions. More specifically, we construct $\mathbb{Z}$-bases for them in five special infinite families of cases. We also derive some results about the corresponding module of relations (in one family of cases, we show that the module of Ennola relations is cyclic). The paper is based upon the thesis [6], which builds upon the results of the paper [2].
DOI : 10.5817/AM2017-4-221
Classification : 11R20
Keywords: circular units; abelian fields; four ramified primes; Ennola relations 
@article{10_5817_AM2017_4_221,
     author = {Sedl\'a\v{c}ek, Vladim{\'\i}r},
     title = {Circular units of real abelian fields with four ramified primes},
     journal = {Archivum mathematicum},
     pages = {221--252},
     year = {2017},
     volume = {53},
     number = {4},
     doi = {10.5817/AM2017-4-221},
     mrnumber = {3733068},
     zbl = {06819527},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2017-4-221/}
}
TY  - JOUR
AU  - Sedláček, Vladimír
TI  - Circular units of real abelian fields with four ramified primes
JO  - Archivum mathematicum
PY  - 2017
SP  - 221
EP  - 252
VL  - 53
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2017-4-221/
DO  - 10.5817/AM2017-4-221
LA  - en
ID  - 10_5817_AM2017_4_221
ER  - 
%0 Journal Article
%A Sedláček, Vladimír
%T Circular units of real abelian fields with four ramified primes
%J Archivum mathematicum
%D 2017
%P 221-252
%V 53
%N 4
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2017-4-221/
%R 10.5817/AM2017-4-221
%G en
%F 10_5817_AM2017_4_221
Sedláček, Vladimír. Circular units of real abelian fields with four ramified primes. Archivum mathematicum, Tome 53 (2017) no. 4, pp. 221-252. doi: 10.5817/AM2017-4-221

[1] Dohmae, K.: A note on Sinnott’s index formula. Acta Arith. 82 (1997), 57–67. | DOI | MR | Zbl

[2] Kučera, R., Salami, A.: Circular units of an abelian field ramified at three primes. J. Number Theory 163 (2016), 296–315. DOI:  | DOI | MR

[3] Lettl, G.: A note on Thaine’s circular units. J. Number Theory 35 (1990), 224– 226. DOI:  | DOI | MR | Zbl

[4] Rubin, K.: Global units and ideal class groups. Invent. Math. 89 (1987), 511–526. | DOI | Zbl

[5] Salami, A.: Bases of the group of cyclotomic units of some real abelian extension. Ph.D. thesis, Université Laval Québec, 2014.

[6] Sedláček, V.: Circular units of abelian fields. Master's thesis, Masaryk University, Faculty of Science, Brno, 2017, [online], [cit. 2017-07-17].

[7] Sinnott, W.: On the Stickelberger ideal and the circular units of an abelian field. Invent. Math. 62 (1980/81), 181–234. | DOI | MR | Zbl

[8] Thaine, F.: On the ideal class groups of real abelian number fields. Ann. of Math. (2) 128 (1988), 1–18. | MR | Zbl

Cité par Sources :