Alexandra Shlapentokh (East Carolina University)

Hilbert's Tenth Problem

• Gebundenes Buch

Produktbeschreibung

Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.

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Produktdetails

• New Mathematical Monographs
• Verlag: Cambridge University Press
• Seitenzahl: 336
• Erscheinungstermin: 9. November 2006
• Englisch
• Abmessung: 235mm x 157mm x 23mm
• Gewicht: 676g
• ISBN-13: 9780521833608
• ISBN-10: 0521833604
• Artikelnr.: 22597392

Autorenporträt

Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.

Inhaltsangabe

1. Introduction
2. Diophantine classes: definition and basic facts
3. Diophantine equivalence and diophantine decidability
4. Integrality at finitely many primes and divisibility of order at infinitely many primes
5. Bound equations for number fields and their consequences
6. Units of rings of W-integers of norm 1
7. Diophantine classes over number fields
8. Diophantine undecidability of function fields
9. Bounds for function fields
10. Diophantine classes over function fields
11. Mazur's conjectures and their consequences
12. Results of Poonen
13. Beyond global fields
A. Recursion theory
B. Number theory
Bibliography
Index.