Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields - New Mathematical Monographs 7 (Hardback)
  • Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields - New Mathematical Monographs 7 (Hardback)
zoom

Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields - New Mathematical Monographs 7 (Hardback)

(author)
£72.00
Hardback 330 Pages / Published: 09/11/2006
  • We can order this

Usually despatched within 3 weeks

  • This item has been added to your basket
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.

Publisher: Cambridge University Press
ISBN: 9780521833608
Number of pages: 330
Weight: 588 g
Dimensions: 228 x 152 x 23 mm


MEDIA REVIEWS
"Shlapentokh offers the first synthesis of the new wave of work, including exciting recent results of B.Poonen that come as close as anyone can yet to extending Matiyesevich's theorem in the desired way." D.V. Feldman, University of New Hampshire for CHOICE
"It gives a very comprehensive survey of what is known so far about undecidability and Diophantine definability for these rings..." Jeroen Demeyer, Mathematical Reviews

You may also be interested in...

Numbers: A Very Short Introduction
Added to basket
Introduction to Analytic Number Theory
Added to basket
The Higher Arithmetic
Added to basket
Number Theory
Added to basket
£69.99
Paperback
Euclid's Elements
Added to basket
£21.99
Paperback
A Comprehensive Course in Number Theory
Added to basket
Elementary Number Theory
Added to basket
Love and Math
Added to basket
£18.99
Hardback
An Introduction to the Theory of Numbers
Added to basket
A Mathematical Tapestry
Added to basket
As Easy As Pi
Added to basket
£6.99
Paperback
Euclid's Elements
Added to basket
£31.99
Hardback
p-adic Numbers
Added to basket
Single Digits
Added to basket
£21.00
Hardback

Reviews

Please sign in to write a review

Your review has been submitted successfully.