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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
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
2007-10-22 17:50:59
date last changed
2017-03-16 14:24:01
@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},
  keyword      = {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},
  volume       = {272},
  year         = {2004},
}