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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
OUR PRICE: $45.59  

Binding Type: Paperback - See All Available Formats & Editions
Published: June 2020
Qty:
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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