Skip to content
Register Sign in Wishlist
Look Inside Many Variations of Mahler Measures

Many Variations of Mahler Measures
A Lasting Symphony

Part of Australian Mathematical Society Lecture Series

  • Publication planned for: July 2020
  • availability: Not yet published - available from July 2020
  • format: Paperback
  • isbn: 9781108794459


Add to wishlist

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne–Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.

    • Bridges the gap between the arithmetic theory of algebraic numbers and complex analysis
    • Displays the source of general connections between regulators and the values of L-functions
    • Gives numerous applications to concrete number-theoretical problems of hypergeometric and modular functions
    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

    • Publication planned for: July 2020
    • format: Paperback
    • isbn: 9781108794459
    • dimensions: 228 x 152 mm
    • contains: 7 b/w illus. 115 exercises
    • availability: Not yet published - available from July 2020
  • Table of Contents

    1. Some basics
    2. Lehmer's problem
    3. Multivariate setting
    4. The dilogarithm
    5. Differential equations for families of Mahler measures
    6. Random walk
    7. The regulator map for $K_2$ of curves
    8. Deninger's method for multivariate polynomials
    9. The Rogers–Zudilin method
    10. Modular regulators
    Appendix. Motivic cohomology and regulator maps
    Author Index
    Subject index.

  • Authors

    François Brunault, Ecole Normale Supérieure, Lyon
    François Brunault is Associate Professor at École Normale Supérieure, Lyon in France, and is a member of the Mathematical Society of France. He is an arithmetic geometer with interest in elliptic curves, modular forms and L-functions, both from a theoretical and explicit point of view.

    Wadim Zudilin, Radboud Universiteit Nijmegen
    Wadim Zudilin is Professor of Pure Mathematics at Radboud University Nijmegen, known for his results that make use of special functions in number theory, in particular, about the irrationality for the values of Riemann's zeta function at positive integers. He co-authored the book Neverending Fractions: An Introduction to Continued Fractions (Cambridge, 2014).

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.