Francois Brunault

Many Variations of Mahler Measures (eBook, PDF)

A Lasting Symphony

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 14. Mai 2020
• Englisch
• ISBN-13: 9781108889193
• Artikelnr.: 66181780

Autorenporträt

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.

Inhaltsangabe

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.