Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields - Couverture rigide

Livre 4 sur 31: New Mathematical Monographs

Shlapentokh, Alexandra

 
9780521833608: Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields
Couverture rigide
ISBN 10 : 0521833604 ISBN 13 : 9780521833608
Editeur : Cambridge University Press, 2006

Synopsis

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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À propos de l?auteur

Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2006
Langue
anglais
ISBN 10 
0521833604
ISBN 13 
9780521833608
Reliure
Relié
Numéro d'édition
1
Nombre de pages
330
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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