On Some Applications of Diophantine Approximations: A translation of C.L. Siegel’s Über einige Anwendungen diophantischer Approximationen, with a commentary ... Normale Superiore Book 2) (English Edition)

This book consists mainly of the translation by C. Fuchs of the 1929 landmark paper Uber 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 ve rsion 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.