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 ...
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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.
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Add this copy of Hilbert's Tenth Problem: Diophantine Classes and to cart. $40.00, like new condition, Sold by Powell's Books Chicago rated 5.0 out of 5 stars, ships from Chicago, IL, UNITED STATES, published 2006 by Cambridge University Press.
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Like New in Like New jacket. Size: 6x0x8; A firm and square hardback with sharp corners and strong joints, complete with original dustjacket, just showing a few very minor rubs. Hence a non-text page has a small 'damaged' stamp. Despite such this book is actually in nearly new condition and appears unread. Thus the contents are crisp, fresh and tight. Also, no pen-marks and not from a library so no such stamps or labels. Now offered for sale at a very sensible price.
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