Click Here to Download: https://ouo.io/H0aYIc On Some Applications of Diophantine Approximations A translation of C.L. Siegel’s Über einige Anwendungen diophantischer Approximationen, with a commentary by C. Fuchs and U. Zannier) By: Umberto Zannier Publisher: Edizioni della Normale Print ISBN: 9788876425196, 8876425195 eText ISBN: 9788876425202, 8876425209 Copyright year: 2014 Format: PDF Available from $ 39.99 USD SKU 9788876425202 This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper Über einige Anwendungen diophantischer Approximationen by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.
