Approximation to real numbers by cubic algebraic integers. II
成果类型：
Article
署名作者：
Roy, D
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2003.158.1081
发表日期：
2003
页码：
1081-1087
关键词：
摘要：
It has been conjectured for some time that, for any integer n greater than or equal to 2, any real number epsilon > 0 and any transcendental real number xi, there would exist infinitely many algebraic integers a of degree at most n with the property that \xi - alpha\ less than or equal to H(alpha)(-n+epsilon), where H(alpha) denotes the height of alpha. Although this is true for n = 2, we show here that, for n = 3, the optimal exponent of approximation is not 3 but (3 + root5)/2 similar or equal to 2.618.