Lecture Notes on Diophantine Analysis : With an Appendix by Francesco Amoroso / Umberto Zannier.

Format:

Book

Author/Creator:

Zannier, Umberto, author.

Language:

English

Subjects (All):

Mathematical analysis.

Mathematical analysis--Congresses.

Physical Description:

1 online resource

Place of Publication:

Berlin : EMS Press, 2024.

Summary:

The present book is a new, substantially enlarged, version of a previous set of lecture notes on diophantine analysis, published first in 2008, and then in revised form a few years later, by the Edizioni della Scuola Normale. The content mixes a number of rather classical results on diophantine equations and diophantine approximation, with the basic theory of heights and a few more recent results and applications of it. The exposition has been generally kept at an elementary and essentially self-contained level, focusing on some main ideas rather than finer technical results which can be obtained by similar methods. In fact, the book is addressed also to readers outside the relevant fields, with the hope that also more expert readers might find something relevant to them.

Contents:

Frontmatter

Preface to the second edition

Preface

Notation and conventions

Contents

Introduction

Some classical diophantine examples

Thue's equations and rational approximations

Heights and diophantine equations over number fields

Heights on subvarieties of Gmn

The S-unit equation

Index

References

Francesco Amoroso: Lower bounds for the height

References for the appendix.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783985475773