Alexandra Shlapentokh's Hilbert's Tenth Problem: Diophantine Classes and Extensions PDF

By Alexandra Shlapentokh

within the past due 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 recommendations. Hilbert gave discovering such an set of rules as challenge quantity ten on an inventory he offered at a global congress of mathematicians in 1900. therefore the matter, which has develop into referred to as Hilbert's 10th challenge, used to be proven to be unsolvable. This publication provides an account of effects extending Hilbert's 10th challenge to integrally closed subrings of world fields together with, within the functionality box case, the fields themselves. whereas written from the perspective of Algebraic quantity idea, the ebook contains chapters on Mazur's conjectures on topology of rational issues and Poonen's elliptic curve process 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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