Many Variations of Mahler Measures
A Lasting Symphony
AUD$75.95 inc GST
Part of Australian Mathematical Society Lecture Series
- Authors:
- François Brunault, Ecole Normale Supérieure, Lyon
- Wadim Zudilin, Radboud Universiteit Nijmegen
- Date Published: May 2020
- availability: Available
- format: Paperback
- isbn: 9781108794459
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inc GST
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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.
Read more- 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
Reviews & endorsements
'… the book will serve as a great introduction to the subject of Mahler's measure, in some of its manifold variations, with a special focus on its links with special values of L-functions. It is particularly suited for a student or research seminar, as well as for individual work, because of its concise nature, which emphasizes the most important points of the theory, while not leaving out crucial details when needed.' Riccardo Pengo, zbMATH
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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
References
Author Index
Subject index.
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