---
res:
bibo_abstract:
- We investigate the distribution of real algebraic numbers of a fixed degree that
have a close conjugate number, with the distance between the conjugate numbers
being given as a function of their height. The main result establishes the ubiquity
of such algebraic numbers in the real line and implies a sharp quantitative bound
on their number. Although the main result is rather general, it implies new estimates
on the least possible distance between conjugate algebraic numbers, which improve
recent bounds obtained by Bugeaud and Mignotte. So far, the results a la Bugeaud
and Mignotte have relied on finding explicit families of polynomials with clusters
of roots. Here we suggest a different approach in which irreducible polynomials
are implicitly tailored so that their derivatives assume certain values. We consider
some applications of our main theorem, including generalisations of a theorem
of Baker and Schmidt and a theorem of Bernik, Kleinbock and Margulis in the metric
theory of Diophantine approximation.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Victor
foaf_name: Beresnevich, Victor
foaf_surname: Beresnevich
- foaf_Person:
foaf_givenName: Vasili
foaf_name: Bernik, Vasili
foaf_surname: Bernik
- foaf_Person:
foaf_givenName: Friedrich
foaf_name: Götze, Friedrich
foaf_surname: Götze
foaf_workInfoHomepage: http://www.librecat.org/personId=10518
bibo_doi: 10.1112/S0010437X10004860
bibo_issue: '5'
bibo_volume: 146
dct_date: 2010^xs_gYear
dct_identifier:
- UT:000282349100003
dct_isPartOf:
- http://id.crossref.org/issn/0010-437X
dct_language: eng
dct_publisher: LONDON MATH SOC@
dct_subject:
- Diophantine approximation
- approximation by
- polynomial root separation
- algebraic numbers
dct_title: The distribution of close conjugate algebraic numbers@
...