| Title:
|
Circular units of real abelian fields with four ramified primes (English) |
| Author:
|
Sedláček, Vladimír |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
221-252 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
circular units |
| Keyword:
|
abelian fields |
| Keyword:
|
four ramified primes |
| Keyword:
|
Ennola relations |
| MSC:
|
11R20 |
| idZBL:
|
Zbl 06819527 |
| idMR:
|
MR3733068 |
| DOI:
|
10.5817/AM2017-4-221 |
| . |
| Date available:
|
2017-11-22T09:42:55Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146984 |
| . |
| Reference:
|
[1] Dohmae, K.: A note on Sinnott’s index formula.Acta Arith. 82 (1997), 57–67. Zbl 0887.11046, MR 1475766, 10.4064/aa-82-1-57-67 |
| Reference:
|
[2] Kučera, R., Salami, A.: Circular units of an abelian field ramified at three primes.J. Number Theory 163 (2016), 296–315. DOI: http://dx.doi.org/https://doi.org/10.1016/j.jnt.2015.11.023 MR 3459572, 10.1016/j.jnt.2015.11.023 |
| Reference:
|
[3] Lettl, G.: A note on Thaine’s circular units.J. Number Theory 35 (1990), 224– 226. DOI: http://dx.doi.org/http://dx.doi.org/10.1016/0022-314X(90)90115-8 Zbl 0705.11064, MR 1057325, 10.1016/0022-314X(90)90115-8 |
| Reference:
|
[4] Rubin, K.: Global units and ideal class groups.Invent. Math. 89 (1987), 511–526. Zbl 0628.12007, 10.1007/BF01388983 |
| Reference:
|
[5] Salami, A.: Bases of the group of cyclotomic units of some real abelian extension.Ph.D. thesis, Université Laval Québec, 2014. |
| Reference:
|
[6] Sedláček, V.: Circular units of abelian fields.Master's thesis, Masaryk University, Faculty of Science, Brno, 2017, [online], [cit. 2017-07-17]. |
| Reference:
|
[7] Sinnott, W.: On the Stickelberger ideal and the circular units of an abelian field.Invent. Math. 62 (1980/81), 181–234. Zbl 0465.12001, MR 0595586, 10.1007/BF01389158 |
| Reference:
|
[8] Thaine, F.: On the ideal class groups of real abelian number fields.Ann. of Math. (2) 128 (1988), 1–18. Zbl 0665.12003, MR 0951505 |
| . |
