Many Variations of Mahler Measures: A Lasting Symphony

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.

Author: François Brunault, Wadim Zudilin
Publisher: Cambridge University Press
Published: 06/18/2020
Pages: 180
Binding Type: Paperback
Weight: 0.60lbs
Size: 8.86h x 6.11w x 0.42d
ISBN13: 9781108794459
ISBN10: 1108794459
BISAC Categories:
- Mathematics | Number Theory