Lecture Notes (Scuola Normale Superiore)

Lecture Notes on Diophantine Analysis

Authors: Zannier, Umberto

  • Examines 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
see more benefits

Buy this book

eBook $24.99
price for USA (gross)
  • ISBN 978-88-7642-517-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $34.95
price for USA
  • ISBN 978-88-7642-341-3
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
About this Textbook

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)

Table of contents (5 chapters)

  • Some classical diophantine examples

    Zannier, Umberto

    Pages 1-35

  • Thue’s equations and rational approximations

    Zannier, Umberto

    Pages 37-76

  • Heights and diophantine equations over number fields

    Zannier, Umberto

    Pages 77-134

  • Heights on subvarieties of G m n

    Zannier, Umberto

    Pages 135-178

  • The S-unit equation

    Zannier, Umberto

    Pages 179-195

Buy this book

eBook $24.99
price for USA (gross)
  • ISBN 978-88-7642-517-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $34.95
price for USA
  • ISBN 978-88-7642-341-3
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Lecture Notes on Diophantine Analysis
Authors
Series Title
Lecture Notes (Scuola Normale Superiore)
Series Volume
8
Copyright
2014
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
eBook ISBN
978-88-7642-517-2
DOI
10.1007/978-88-7642-517-2
Softcover ISBN
978-88-7642-341-3
Edition Number
1
Number of Pages
XVI, 239
Topics