Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Hilbert's Tenth Problem
  • Cited by 16
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      14 October 2009
      09 November 2006
      ISBN:
      9780511542954
      9780521833608
      DOI:
      https://doi.org/10.1017/CBO9780511542954
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.588kg, 330 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Number Theory
      Series:
      New Mathematical Monographs (7)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Number Theory
    Series:
    New Mathematical Monographs (7)
    Information

    Book description

    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.

    Reviews

    "Shlapentokh offers the first synthesis of the new wave of work, including exciting recent results of B.Poonen that come as close as anyone can yet to extending Matiyesevich's theorem in the desired way."
    D.V. Feldman, University of New Hampshire for CHOICE

    "It gives a very comprehensive survey of what is known so far about undecidability and Diophantine definability for these rings..."
    Jeroen Demeyer, Mathematical Reviews

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.