Many Variations of Mahler Measures: A Lasting Symphony

ISBN-13: 9781108794459 / Angielski / Miękka / 2020 / 180 str.

Francois Brunault; Wadim Zudilin

Opis

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

Recenzje

'… 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

Spis treści

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.