Zannier 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)
1. Auflage 2015
ISBN: 978-88-7642-520-2
Verlag: Edizioni della Normale
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2, 157 Seiten, eBook

Reihe: Publications of the Scuola Normale Superiore

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.

Zielgruppe

Research

Autoren/Hrsg.

Zannier, Umberto

Inhaltsverzeichnis

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.