Items related to Hilbert's Tenth Problem: Diophantine Classes and...

Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields (New Mathematical Monographs, Series Number 7) - Hardcover

Book 4 of 31: New Mathematical Monographs

Shlapentokh, Alexandra

 
9780521833608: Hilbert's Tenth Problem: Diophantine Classes and Extensions to Global Fields (New Mathematical Monographs, Series Number 7)
Hardcover
ISBN 10: 0521833604 ISBN 13: 9780521833608
Publisher: 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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About the Author

Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
2006
Language
English
ISBN 10 
0521833604
ISBN 13 
9780521833608
Binding
Hardcover
Edition number
1
Number of pages
330