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Technical Lectures on Diophantine Approximations Part 1
Posted on 2010-04-14
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More Lectures on Diophantine Approximations Part 1: g-adic numbers and Roth's theorem. Prepared from the notes by R. P. Bambah of my lectures given at the University of Notre Dame in the Fall of 1957. 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. My Links Download Link (Uploading.com) To thank me use my links, please!
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