Skip to content
Register Sign in Wishlist

Approximation by Algebraic Numbers


Part of Cambridge Tracts in Mathematics

  • Date Published: December 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521045674

£ 64.99

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler's conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.

    • Broad treatment accessible to graduate students and non-specialists
    • Rich and comprehensive list of references
    • Collection of 50 open problems
    Read more

    Reviews & endorsements

    'The book is written in a relaxed style, and begins with some accessible introductory chapters … It is nicely written and well explained, and proofs in the main are given in full. this book is certainly suitable for a non-expert in the area, or as a graduate course for an advanced student … All in all, this is a very nice book.' Bulletin of the London Mathematical Society

    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: December 2007
    • format: Paperback
    • isbn: 9780521045674
    • length: 292 pages
    • dimensions: 227 x 153 x 20 mm
    • weight: 0.435kg
    • contains: 40 exercises
    • availability: Available
  • Table of Contents

    Frequently used notation
    1. Approximation by rational numbers
    2. Approximation to algebraic numbers
    3. The classifications of Mahler and Koksma
    4. Mahler's conjecture on S-numbers
    5. Hausdorff dimension of exceptional sets
    6. Deeper results on the measure of exceptional sets
    7. On T-numbers and U-numbers
    8. Other classifications of real and complex numbers
    9. Approximation in other fields
    10. Conjectures and open questions
    Appendix A. Lemmas on polynomials
    Appendix B. Geometry of numbers

  • Author

    Yann Bugeaud, Université de Strasbourg

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

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 ×

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.