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Carte Hilbert's Tenth Problem Alexandra Shlapentokh

Hilbert's Tenth Problem

Diophantine Classes and Extensions to Global Fields

Autor: Alexandra Shlapentokh
Limbă: engleză
Legare: Copertă tare
Editura: Cambridge University Press
Disponibilitate: În depozitul extern
Expediem în 9-15 zile
847.37 lei
In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that th...

Informații despre carte

Autor
Alexandra Shlapentokh
Limbă
engleză
Legare
Carte - Copertă tare
Publicat
2006
Pagini
330
EAN
9780521833608
ISBN
0521833604
Enbook ID
02045940
Editura
Cambridge University Press
Greutate
588
Dimensiuni
158 x 233 x 23

Descriere completă

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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