Skip to content
Register Sign in Wishlist

Hilbert's Tenth Problem
Diophantine Classes and Extensions to Global Fields


Part of New Mathematical Monographs

  • Date Published: November 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521833608

£ 99.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • Looks at the subject from the point of view of Algebraic Number Theory
    • Also includes information on Mazur's Conjectures and Poonen's elliptic curve method
    • Suitable for graduate students
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: November 2006
    • format: Hardback
    • isbn: 9780521833608
    • length: 330 pages
    • dimensions: 233 x 158 x 23 mm
    • weight: 0.588kg
    • contains: 18 b/w illus.
    • availability: Available
  • Table of Contents

    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

  • Author

    Alexandra Shlapentokh, East Carolina University
    Alexandra Shlapentokh is Professor of Mathematics at East Carolina University.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.