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epsilon-Pisot numbers in any real algebraic number field are relatively dense

Fan, AH and Schmeling, Jörg LU (2004) In Journal of Algebra 272(2). p.470-475
Abstract
An algebraic integer is called an epsilon-Pisot number (epsilon > 0) if its Galois conjugates have absolute value less then epsilon. Let K be any real algebraic number field. We prove that the subset of K consisting of epsilon-Pisot numbers which have the same degree as that of the field is relatively dense in the real line R. This has some applications to non-stationary products of random matrices involving Salem numbers. (C) 2004 Elsevier Inc. All rights reserved.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
real algebraic number fields, PV-numbers, Salem numbers
in
Journal of Algebra
volume
272
issue
2
pages
470 - 475
publisher
Elsevier
external identifiers
  • wos:000188369100005
  • scopus:0742306753
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2003.09.027
language
English
LU publication?
yes
id
672ec121-277a-44c1-98c5-4bdd707b389d (old id 289045)
date added to LUP
2016-04-01 12:17:35
date last changed
2022-01-27 01:39:30
@article{672ec121-277a-44c1-98c5-4bdd707b389d,
  abstract     = {{An algebraic integer is called an epsilon-Pisot number (epsilon > 0) if its Galois conjugates have absolute value less then epsilon. Let K be any real algebraic number field. We prove that the subset of K consisting of epsilon-Pisot numbers which have the same degree as that of the field is relatively dense in the real line R. This has some applications to non-stationary products of random matrices involving Salem numbers. (C) 2004 Elsevier Inc. All rights reserved.}},
  author       = {{Fan, AH and Schmeling, Jörg}},
  issn         = {{0021-8693}},
  keywords     = {{real algebraic number fields; PV-numbers; Salem numbers}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{470--475}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Algebra}},
  title        = {{epsilon-Pisot numbers in any real algebraic number field are relatively dense}},
  url          = {{http://dx.doi.org/10.1016/j.jalgebra.2003.09.027}},
  doi          = {{10.1016/j.jalgebra.2003.09.027}},
  volume       = {{272}},
  year         = {{2004}},
}