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Lecture Notes on Diophantine Analysis

  • Textbook
  • © 2014

Overview

Authors:
  1. Umberto Zannier

    1. Scuola Normale Superiore, Pisa, Italy

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  • Treats classical diophantine equations but also modern Diophantine issues
  • Uses ‘concrete’ methods but also offers modern abstract interpretations
  • Contains a large number of Supplements and hinted exercises in several different directions, which are difficult to find in a single book
  • Occasionally contains viewpoints and results which do not appear elsewhere

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 8)

Part of the book sub series: Lecture Notes (Scuola Normale Superiore) (LNSNS)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Some classical diophantine examples

    • Umberto Zannier
    Pages 1-35

  3. Thue’s equations and rational approximations

    • Umberto Zannier
    Pages 37-76

  4. Heights and diophantine equations over number fields

    • Umberto Zannier
    Pages 77-134

  5. Heights on subvarieties of G nm

    • Umberto Zannier
    Pages 135-178

  6. The S-unit equation

    • Umberto Zannier
    Pages 179-195

  7. Back Matter

    Pages 197-237
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Keywords

About this book

These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.

Reviews

From the reviews:

“This set of lectures originates from an introductory course given by the author at the Scuola Normale Superiore Pisa in 2006-2007 on Diophantine analysis. … provide a lot of further information on these topics, including recent developments and open problem. Hence this booklet starts at an elementary level … and reaches the limit of our current knowledge on all these topics. … a useful addition to the literature on this fashionable topic, both for the beginner and for the researcher.” (Michel Waldschmidt, Zentralblatt MATH, Vol. 1186, 2010)

Authors and Affiliations

  • Scuola Normale Superiore, Pisa, Italy

    Umberto Zannier

Bibliographic Information

  • Book Title: Lecture Notes on Diophantine Analysis

  • Authors: Umberto Zannier

  • Series Title: Publications of the Scuola Normale Superiore

  • DOI: https://doi.org/10.1007/978-88-7642-517-2

  • Publisher: Edizioni della Normale Pisa

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

  • Copyright Information: Edizioni della Normale 2014

  • Softcover ISBN: 978-88-7642-341-3Published: 31 March 2009

  • eBook ISBN: 978-88-7642-517-2Published: 05 May 2015

  • Series ISSN: 2239-1460

  • Series E-ISSN: 2532-1668

  • Edition Number: 1

  • Number of Pages: XVI, 239

  • Topics: Analysis

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