On Some Applications of Diophantine Approximations Zoom

On Some Applications of Diophantine Approximations

edited by Umberto Zannier

pp. x-157

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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 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.

Additional Information

Additional Information

Title On Some Applications of Diophantine Approximations
Author (display) No
Editing/translations edited by Umberto Zannier
ISBN 978-88-7642-519-6
Publishing year 2014
Subject Fisica e storia della fisica
Buy link http://www.springer.com/birkhauser/mathematics/scuola+normale+superiore/book/978-88-7642-519-6
Notes No