Happy Holidays! Over 120,000 eBooks at just 19.99 each— Pick a favorite today

Monographs (Scuola Normale Superiore)

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.)

  • 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
see more benefits

Buy this book

eBook 20,22 €
price for Spain (gross)
  • ISBN 978-88-7642-520-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 27,04 €
price for Spain (gross)
  • ISBN 978-88-7642-519-6
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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

“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)

  • On some applications of Diophantine approximations

    Fuchs, Clemens

    Pages 1-80

    Preview Buy Chapter 30,19 €
  • Über einige Anwendungen diophantischer Approximationen

    Siegel, Carl L.

    Pages 81-138

    Preview Buy Chapter 30,19 €
  • Integral points on curves: Siegel’s theorem after Siegel’s proof

    Fuchs, Clemens (et al.)

    Pages 139-157

    Preview Buy Chapter 30,19 €

Buy this book

eBook 20,22 €
price for Spain (gross)
  • ISBN 978-88-7642-520-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 27,04 €
price for Spain (gross)
  • ISBN 978-88-7642-519-6
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
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
  • 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