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Number Theory III: Diophantine Geometry
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Number Theory III: Diophantine Geometry Hardback - 1991 - 1991st Edition

by Serge Lang

  • New
  • Hardcover

Description

Hardback. New. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q.
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Details

  • Title Number Theory III: Diophantine Geometry
  • Author Serge Lang
  • Binding Hardback
  • Edition number 1991st
  • Edition 1991
  • Condition New
  • Pages 296
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Date 1991-06-27
  • Features Bibliography
  • Bookseller's Inventory # B9783540530046
  • ISBN 9783540530046 / 3540530045
  • Weight 1.36 lbs (0.62 kg)
  • Dimensions 9.21 x 6.14 x 0.75 in (23.39 x 15.60 x 1.91 cm)
  • Library of Congress Catalog Number 91017718
  • Dewey Decimal Code 512.7

From the publisher

Serge Lang is well-known as a mathematician and as an author of mathematical books, some of which have become standard texts. The current volume is the first to appear of the volumes covering number theory. The book gives an accessible presentation of an area of number theory that has recently had very important successes.

From the rear cover

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 thisbook 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 fr Mathematik, 1993

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