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)
Editors: Zannier, Umberto (Ed.)
Free Preview- Presents for the first time in English a landmark paper by Siegel which introduced most important ideas in the realm of Diophantine approximation and its applications
- Presents the ideas of Siegel in original form, contrary to most modern proofs given in English
- Includes an article commenting on mathematical evolution after Siegel’s paper
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- About this book
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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.
- Reviews
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“This book contains both Siegel’s original paper in German and an English translation. … this is a fundamental paper, well worth reading. … It will be of great interest to mathematicians working in transcendence theory and Diophantine approximation, and to anyone interested in the history of mathematics in the early 20th century.” (Fernando Q. Gouvêa, MAA Reviews, June, 2015)
- Table of contents (3 chapters)
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On some applications of Diophantine approximations
Pages 1-80
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Über einige Anwendungen diophantischer Approximationen
Pages 81-138
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Integral points on curves: Siegel’s theorem after Siegel’s proof
Pages 139-157
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Table of contents (3 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- On Some Applications of Diophantine Approximations
- Book Subtitle
- A translation of C.L. Siegel’s Über einige Anwendungen diophantischer Approximationen, with a commentary by C. Fuchs and U. Zannier)
- Editors
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- Umberto Zannier
- Series Title
- Monographs (Scuola Normale Superiore)
- Series Volume
- 2
- Copyright
- 2014
- Publisher
- Edizioni della Normale
- Copyright Holder
- Scuola Normale Superiore Pisa
- eBook ISBN
- 978-88-7642-520-2
- DOI
- 10.1007/978-88-7642-520-2
- Softcover ISBN
- 978-88-7642-519-6
- Edition Number
- 1
- Number of Pages
- X, 157
- Topics
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