2002/10/24 by Damien Roy
Mathematics · #math.NT #msc:11J13 #msc:11J04
published as C. R. Acad. Sci. Paris, Ser. I 336 (2003), 1-6. · 6 pages
arxiv created 2002/10/24 · arxiv updated 2009/11/30
In 1969, H. Davenport and W. Schmidt established a measure of simultaneous approximation for a real number ξand its square by rational numbers with the same denominator, assuming only that ξis not rational nor quadratic over Q. Here, we show by an example, that this measure is optimal. We also indicate several properties of the numbers for which this measure is optimal, in particular with respect to approximation by algebraic integers of degree at most three.