Lectures On Diophantine Approximations
by Kurt Mahler /
1961 / English / PDF
9.4 MB Download
In 1955, K. F. Roth obtained his theorem on the rational approximations of a real algebraic number. It was immediately clear that his method should also work for p-adic algebraic numbers, for Roth's method could clearly be combined with that of my old papers. Some interesting work of this kind was in fact carried out by D. Ridout, a student of Roth. In the second part of these lectures I shall try to go rather further in this direction. As the proofs will show, the p-adic numbers, and more generally the g-adic numbers form an important tool in these investigations but one form of the final result will be again free of such numbers and will state a property of rational numbers only.
