Skip to main content
SpringerLink
Log in
Book cover

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)

  • Book
  • © 2014
Download book PDF

Overview

Editors:
  1. Umberto Zannier

    1. Scuola Normale Superiore, Pisa, Italia

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • 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

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 2)

Part of the book sub series: Monographs (Scuola Normale Superiore) (MSNS)

Buy print copy

Softcover Book USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Table of contents (3 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. On some applications of Diophantine approximations

    • Clemens Fuchs
    Pages 1-80
    Download chapter PDF

  3. Über einige Anwendungen diophantischer Approximationen

    • Carl L. Siegel
    Pages 81-138
    Download chapter PDF

  4. Integral points on curves: Siegel’s theorem after Siegel’s proof

    • Clemens Fuchs, Umberto Zannier
    Pages 139-157
    Download chapter PDF

  5. Back Matter

    Pages 159-161
    Download chapter PDF
Back to top

Keywords

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)

Editors and Affiliations

  • Scuola Normale Superiore, Pisa, Italia

    Umberto Zannier

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: Publications of the Scuola Normale Superiore

  • DOI: https://doi.org/10.1007/978-88-7642-520-2

  • Publisher: Edizioni della Normale Pisa

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Scuola Normale Superiore Pisa 2014

  • Softcover ISBN: 978-88-7642-519-6Published: 27 January 2015

  • eBook ISBN: 978-88-7642-520-2Published: 13 February 2015

  • Series ISSN: 2239-1460

  • Series E-ISSN: 2532-1668

  • Edition Number: 1

  • Number of Pages: X, 157

  • Topics: Number Theory

Publish with us

Policies and ethics

Back to top

Search

Navigation