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Hilbert's Tenth Problem - Diophantine Classes and Extensions to Global Fields (Hardcover)
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Hilbert's Tenth Problem - Diophantine Classes and Extensions to Global Fields (Hardcover)
Series: New Mathematical Monographs
Expected to ship within 10 - 15 working days
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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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