Download e-book for iPad: Hilbert's Tenth Problem: Diophantine Classes and Extensions by Alexandra Shlapentokh

By Alexandra Shlapentokh

within the overdue sixties Matiyasevich, development at the paintings of Davis, Putnam and Robinson, confirmed that there has been no set of rules to figure out no matter if a polynomial equation in numerous variables and with integer coefficients has integer suggestions. Hilbert gave discovering such an set of rules as challenge quantity ten on a listing he offered at a world congress of mathematicians in 1900. hence the matter, which has turn into often called Hilbert's 10th challenge, was once proven to be unsolvable. This booklet provides an account of effects extending Hilbert's 10th challenge to integrally closed subrings of worldwide fields together with, within the functionality box case, the fields themselves. whereas written from the viewpoint of Algebraic quantity idea, the e-book contains chapters on Mazur's conjectures on topology of rational issues and Poonen's elliptic curve approach for developing a Diophatine version of rational integers over a 'very huge' subring of the sphere of rational numbers.

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Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields (New Mathematical Monographs) by Alexandra Shlapentokh

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