On approximation of real numbers by algebraic numbers of bounded degree

✍ Scribed by Kiryl I. Tsishchanka

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 228 KB
• Volume: 123
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.07.012

✦ Synopsis

Dirichlet proved that for any real irrational number ξ there exist infinitely many rational numbers p/q such that |ξp/q| < q -2 . The correct generalization to the case of approximation by algebraic numbers of degree n, n > 2, is still unknown. Here we prove a result which improves all previous estimates concerning this problem for n > 2.