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Hilbert's Tenth Problem on Hardback by Alexandra Shlapentokh
Hilbert's Tenth Problem on Hardback by Alexandra Shlapentokh
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Hilbert's Tenth Problem

Diophantine Classes and Extensions to Global Fields
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Description

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.

Author Biography:

Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.
Release date Australia
November 9th, 2006
Audience
  • Professional & Vocational
Illustrations
18 Line drawings, unspecified
Pages
330
Dimensions
158x233x23
ISBN-13
9780521833608
Product ID
1772336

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