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Many Variations of Mahler Measures
A Lasting Symphony

AUD$63.95 inc GST

Part of Australian Mathematical Society Lecture Series

  • Date Published: May 2020
  • availability: Available
  • format: Paperback
  • isbn: 9781108794459

AUD$ 63.95 inc GST

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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
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    Product details

    • Date Published: May 2020
    • format: Paperback
    • isbn: 9781108794459
    • length: 180 pages
    • dimensions: 227 x 151 x 10 mm
    • weight: 0.27kg
    • contains: 7 b/w illus. 115 exercises
    • availability: Available
  • 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).

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