epsilon-Pisot numbers in any real algebraic number field are relatively dense
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/289045
- author
- Fan, AH and Schmeling, Jörg LU
- organization
- publishing date
- 2004
- 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}}, }