<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Beresnevich, Victor</style></author><author><style face="normal" font="default" size="100%">Bernik, Vasili</style></author><author><style face="normal" font="default" size="100%">Götze, Friedrich</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The distribution of close conjugate algebraic numbers</style></title><secondary-title><style face="normal" font="default" size="100%">Compositio Mathematica</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Number Theory</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://arxiv.org/abs/0906.4286</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">146</style></volume><pages><style face="normal" font="default" size="100%">1165-1179</style></pages><abstract><style face="normal" font="default" size="100%">The distribution of real algebraic numbers of a fixed degree with a close conjugate is studied. The main result establishes the ubiquity of such algebraic numbers in the real line and implies a sharp quantitative bound on their number. Its consequences contain new estimates on the least possible distance between conjugate algebraic numbers, which improve earlier bounds of Bugeaud and Mignotte. The paper develops a new approach to the problem, while previous results relied on very elementary methods and `hand-made' constructions of specific examples. There is also a range of further applications of the main result which improve earlier theorems of Baker and Schmidt and Bernik, Kleinbock and Margulis.</style></abstract><issue><style face="normal" font="default" size="100%">5</style></issue><custom1><style face="normal" font="default" size="100%">arXiv:0906.4286</style></custom1></record></records></xml>