Description
Book SynopsisThis 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.
Trade Review'… 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
Table of Contents1. 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.
