Alexandra Shlapentokh

Hilbert's Tenth Problem (eBook, PDF)

Diophantine Classes and Extensions to Global Fields

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 9. November 2006
• Englisch
• ISBN-13: 9780511254710
• Artikelnr.: 38205968

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.