Skip to content
Register Sign in Wishlist

Distribution Modulo One and Diophantine Approximation


Part of Cambridge Tracts in Mathematics

  • Date Published: July 2012
  • availability: Available
  • format: Hardback
  • isbn: 9780521111690

£ 62.99

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
  • This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.

    • Assembles for the first time results scattered across the literature
    • Extensive bibliography provides easy links to further reading
    • Provides more than 50 open problems as suggestions for further research
    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: July 2012
    • format: Hardback
    • isbn: 9780521111690
    • length: 316 pages
    • dimensions: 233 x 157 x 21 mm
    • weight: 0.59kg
    • contains: 70 exercises
    • availability: Available
  • Table of Contents

    1. Distribution modulo one
    2. On the fractional parts of powers of real numbers
    3. On the fractional parts of powers of algebraic numbers
    4. Normal numbers
    5. Further explicit constructions of normal and non-normal numbers
    6. Normality to different bases
    7. Diophantine approximation and digital properties
    8. Digital expansion of algebraic numbers
    9. Continued fraction expansions and beta-expansions
    10. Conjectures and open problems
    A. Combinatorics on words
    B. Some elementary lemmata
    C. Measure theory
    D. Continued fractions
    E. Diophantine approximation
    F. Recurrence sequences

  • Resources for

    Distribution Modulo One and Diophantine Approximation

    Yann Bugeaud

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    *This title has one or more locked files and access is given only to lecturers adopting the textbook for their class. We need to enforce this strictly so that solutions are not made available to students. To gain access to locked resources you either need first to sign in or register for an account.

    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email

  • Author

    Yann Bugeaud, Université de Strasbourg
    Yann Bugeaud is a Professor in the Institut de Recherche Mathématique Avancée (IRMA) at the University of Strasbourg, France.

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.