Circular units of real abelian fields with four ramified primes

Vladimír Sedláček

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 4, page 221-252
  • ISSN: 0044-8753

Abstract

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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 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].

How to cite

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Sedláček, Vladimír. "Circular units of real abelian fields with four ramified primes." Archivum Mathematicum 053.4 (2017): 221-252. <http://eudml.org/doc/294538>.

@article{Sedláček2017,
abstract = {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].},
author = {Sedláček, Vladimír},
journal = {Archivum Mathematicum},
keywords = {circular units; abelian fields; four ramified primes; Ennola relations},
language = {eng},
number = {4},
pages = {221-252},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Circular units of real abelian fields with four ramified primes},
url = {http://eudml.org/doc/294538},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Sedláček, Vladimír
TI - Circular units of real abelian fields with four ramified primes
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 4
SP - 221
EP - 252
AB - 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].
LA - eng
KW - circular units; abelian fields; four ramified primes; Ennola relations
UR - http://eudml.org/doc/294538
ER -

References

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  1. Dohmae, K., 10.4064/aa-82-1-57-67, Acta Arith. 82 (1997), 57–67. (1997) Zbl0887.11046MR1475766DOI10.4064/aa-82-1-57-67
  2. Kučera, R., Salami, A., 10.1016/j.jnt.2015.11.023, J. Number Theory 163 (2016), 296–315. DOI: http://dx.doi.org/https://doi.org/10.1016/j.jnt.2015.11.023 (2016) MR3459572DOI10.1016/j.jnt.2015.11.023
  3. Lettl, G., 10.1016/0022-314X(90)90115-8, J. Number Theory 35 (1990), 224– 226. DOI: http://dx.doi.org/http://dx.doi.org/10.1016/0022-314X(90)90115-8 (1990) Zbl0705.11064MR1057325DOI10.1016/0022-314X(90)90115-8
  4. Rubin, K., 10.1007/BF01388983, Invent. Math. 89 (1987), 511–526. (1987) Zbl0628.12007DOI10.1007/BF01388983
  5. Salami, A., Bases of the group of cyclotomic units of some real abelian extension, Ph.D. thesis, Université Laval Québec, 2014. (2014) 
  6. Sedláček, V., Circular units of abelian fields, Master's thesis, Masaryk University, Faculty of Science, Brno, 2017, [online], [cit. 2017-07-17]. (2017) 
  7. Sinnott, W., 10.1007/BF01389158, Invent. Math. 62 (1980/81), 181–234. (1980) Zbl0465.12001MR0595586DOI10.1007/BF01389158
  8. Thaine, F., On the ideal class groups of real abelian number fields, Ann. of Math. (2) 128 (1988), 1–18. (1988) Zbl0665.12003MR0951505

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