Many Variations of Mahler Measures: A Lasting Symphony Contributor(s): Brunault, François (Author), Zudilin, Wadim (Author) |
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ISBN: 1108794459 ISBN-13: 9781108794459 Publisher: Cambridge University Press
Binding Type: Paperback - See All Available Formats & Editions Published: June 2020 |
Additional Information |
BISAC Categories: - Mathematics | Number Theory |
Physical Information: 0.42" H x 6.11" W x 8.86" L (0.60 lbs) 180 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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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