Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields

Alexandra Shlapentokh

ISBN 10: 0521833604 / ISBN 13: 9780521833608

Published by Cambridge Univ Pr, 2006

About this Item

1st edition. 320 pages. 9.25x6.25x0.75 inches. In Stock.

Seller Inventory # x-0521833604

Bibliographic Details

• Title: Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields
• Publisher: Cambridge Univ Pr
• Publication Date: 2006
• Language: English
• ISBN 10: 0521833604
• ISBN 13: 9780521833608
• Binding: Hardcover
• Condition: Brand New
• Weight: 0.59 kilograms

About this title

Synopsis

In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers.

About the Author

Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.