Hilbert's tenth problem : diophantine classes and extensions to global fields /

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 int...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Shlapentokh, Alexandra
Format: Electronic eBook
Language:Inglés
Published: Cambridge, UK ; New York : Cambridge University Press, 2006.
Series:New mathematical monographs ; 7.
Subjects:
Hilbert's tenth problem.
Algebraic number theory.
Diophantine equations.
Dixième problème de Hilbert.
Théorie algébrique des nombres.
Équations diophantiennes.
MATHEMATICS > Number Theory.
Algebraic number theory
Diophantine equations
Hilbert's tenth problem
Online Access:Texto completo
Table of Contents:
  • Introduction
  • Diophantine classes: definitions and basic facts
  • Diophantine equivalence and Diophantine decidability
  • Integrality at finitely many primes and divisibility of order at infinitely many primes
  • Bound equations for number fields and their consequences
  • Units of rings of W-integers of norm 1
  • Diophantine classes over number fields
  • Diophantine undecidability of function fields
  • Bounds for function fields
  • Diophantine classes over function fields
  • Mazur's conjectures and their consequences
  • Results of Poonen
  • Beyond global fields
  • Recursion (computability) theory
  • Number theory.

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