Encyclopaedia of Mathematical Sciences

Number Theory III

Diophantine Geometry

Authors: Lang, Serge

Editors: Lang, Serge (Ed.)

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About this book

From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments.

This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics are treated in a nice, coherent way, however not in a historically logical order. ...The author writes "At the moment of writing, the situation is in flux...". That is clear from the scope of this book. In the area described many conjectures, important results, new developments took place in the last 30 years. And still new results come at a breathtaking speed in this rich field. In the introduction the author notices: "I have included several connections of diophantine geometry with other parts of mathematics, such as PDE and Laplacians, complex analysis, and differential geometry. A grand unification is going on, with multiple connections between these fields." Such a unification becomes clear in this beautiful book, which we recommend for mathematicians of all disciplines." Medelingen van het wiskundig genootschap, 1994
"... It is fascinating to see how geometry, arithmetic and complex analysis grow together!..." Monatshefte für Mathematik, 1993

Reviews

From the reviews: "Between number theory and geometry there have been several stimulating influences, and this book records these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication... Although in the series of number theory, this volume is on diophantine geometry, the reader will notice that algebraic geometry is present in every chapter. ...The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Mededelingen van het wiskundig genootschap

Table of contents (10 chapters)

  • Some Qualitative Diophantine Statements

    Gamkrelidze, R. V.

    Pages 1-42

    Preview Buy Chapter 30,19 €
  • Heights and Rational Points

    Gamkrelidze, R. V.

    Pages 43-67

    Preview Buy Chapter 30,19 €
  • Abelian Varieties

    Gamkrelidze, R. V.

    Pages 68-100

    Preview Buy Chapter 30,19 €
  • Faltings’ Finiteness Theorems on Abelian Varieties and Curves

    Gamkrelidze, R. V.

    Pages 101-122

    Preview Buy Chapter 30,19 €
  • Modular Curves Over Q

    Gamkrelidze, R. V.

    Pages 123-142

    Preview Buy Chapter 30,19 €

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-642-58227-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 171,59 €
price for Spain (gross)
  • ISBN 978-3-540-53004-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-540-61223-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Number Theory III
Book Subtitle
Diophantine Geometry
Authors
Editors
  • Serge Lang
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
60
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58227-1
DOI
10.1007/978-3-642-58227-1
Hardcover ISBN
978-3-540-53004-6
Softcover ISBN
978-3-540-61223-0
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XIII, 296
Additional Information
Originally published as volume 60 in the series Encyclopaedia of Mathematical Sciences with the title: Number Theory 3
Topics