Many Variations of Mahler Measures - A Lasting Symphony

A friendly and concise introduction to the Mahler measure - a fascinating subject in contemporary mathematics.

List 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.

About the author

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 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).

Summary

This is a unique overview of a fascinating topic in mathematics – the Mahler measure – and its numerous interconnections with areas such as number theory, analysis, arithmetic geometry, special functions and random walks. The text can be used for graduate courses or self-study, with exercises at varying levels of difficulty.

Product details

• Authors: FRAN OIS BRUNAULT, François Brunault, Francois (Ecole Normale Superieure Brunault, Wadim Zudilin, Wadim (Radboud Universiteit Nijmegen) Zudilin, Zudilin Wadim
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 31.07.2020
• EAN: 9781108794459
• ISBN: 978-1-108-79445-9
• No. of pages: 180
• Series: Australian Mathematical Societ; Australian Mathematical Society Lecture Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; MATHEMATICS / Number Theory, Number Theory