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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Shlapentokh, Alexandra
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2006.
Colección:New mathematical monographs ; 7.
Temas:
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
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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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