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)
Author:   Umberto Zannier
Publisher:   Birkhauser Verlag AG
Edition:   2014 ed.
Volume:   2
ISBN:  

9788876425196


Pages:   157
Publication Date:   27 January 2015
Format:   Paperback
Availability:   In Print   Availability explained
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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)


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Overview

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.

Full Product Details

Author:   Umberto Zannier
Publisher:   Birkhauser Verlag AG
Imprint:   Scuola Normale Superiore
Edition:   2014 ed.
Volume:   2
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.363kg
ISBN:  

9788876425196


ISBN 10:   8876425195
Pages:   157
Publication Date:   27 January 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Preface by C. Fuchs and U. Zannier.- On some applications of Diophantine approximations (a translation by C. Fuchs of C.L. Siegel’s Über einige Anwendungen diophantischer Approximationen).- Über einige Anwendungen diophantischer Approximationen (by C.L. Siegel).- Integral points on curves: Siegel’s theorem after Siegel’s proof, by C. Fuchs and U. Zannier.

Reviews

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. Gouvea, MAA Reviews, June, 2015)


“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)


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. Gouvea, MAA Reviews, June, 2015)


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