Many Variations of Mahler Measures: A Lasting Symphony

By Paul Craig

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 1108794459
• ISBN13: 9781108794459
• Release Date: June 2020
• Publisher: Cambridge University Press
• Length: 180 Pages
• Weight: 0.60 lbs.
• Dimensions: 0.4" x 6.1" x 8.9"

Customer Reviews

Like Swigging Half A Bucket of Heroin...

I first read Donaldson's Thomas Covenant series in the early eighties and its efficacy was approximately the equivalent of swigging half a bucket of heroin per book in the series. The man is an outstanding writer but I can see his use of language and description a little hard to take for those new or with entry level experience of the fantasy genre. If you persevere, you will be hugely rewarded believe me! On the other hand,...

After LOTR, this is THE epic fantasy...

there is not really too much that I want to say about the thomas covenant series of books --- I love epic fantasy and after tolkien i think donaldson's 6 books plus of thomas covenant and "the land" is the next best read. truthfully, donaldson wrote the first 2 sets (6 books) in the late 70s --- I have read these 6 books perhaps 30 times since then --- I don't think I need to say much more than that... on top of everything,...

Interesting read but flawed to me....

Overall this is a good trilogy of novels. It is a very character driven series, focusing more on the inner workings of the main character than the plot. Overall, this is a strength to the series, not a weakness. The plot itself is solid enough. Essentially, Thomas Covenant is a leper and an author in our world who is pulled into another realm to help be the savior of the land. Covenant is a very wounded main character,...

Let's Get Down to the Nitty Gritty

I've read all of the reviews here and have something to say to those with negative opinions of this series: for those of you who have relayed your reviews succinctly, I respect your collective opinions. This series is not for everyone. But to those who's reviews seemed to reflect confusion, please give this series another try. You obviously did not 'get it.' This series is not about a fantasy land within which Covenant...

The Land

I started reading Fantasy of course with JRR Tolkien's Lord Of the Rings. My second introduction to the world of Fantasy was Chronicles of Thomas Covenant.Thomas Covenant's by some strange stroke of Fate or perhaps calculated strategy, finds himself in The Land - a place of unsurpassed beauty where Earthpower is a source of power/energy that is tapped on by its people. Covenant is given a message of Doom and asked to deliver...