Heights of Polynomials and Entropy in Algebraic Dynamics / Edition 1

Paperback (Print)
Buy New
Buy New from BN.com
$74.07
Used and New from Other Sellers
Used and New from Other Sellers
from $64.38
Usually ships in 1-2 business days
(Save 28%)
Other sellers (Paperback)
  • All (4) from $64.38   
  • New (4) from $64.38   

Overview

The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number theory and nonlinear dynamics.

"...includes a large body of results on Mahler's measure of the height of a polynomial and the entropy associated with a dynamical system...examples and particular computations are provided."

Read More Show Less

Editorial Reviews

From the Publisher
From the reviews:

"At first sight it would seem exceedingly unlikely that there would be any relation at all between entropy and height. Reality is otherwise: they are very much intertwined, and this is what this unusual and very interesting book is about. … The authors write about all this with erudition and charm … . They have included more than a hundred exercises … ." (M. Hazewinkel, Nieuw Archief voor Wiskunde, Vol. 5/6 (3), 2005)

"It ranges through a number of topics, varying from the elementary to the sophisticated, all featuring polynomials. … this text provides an excellent basis for a beginning postgraduate course, since most of the material is not too demanding and yet it arouses the curiosity to learn more about dynamical systems, algebraic number theory or primality testing. In addition, there are 103 exercises with hints, five useful appendices sketching the prerequisites, and an extensive bibliography … ." (Victor P. Snaith, Bulletin of the London Mathematical Society, Vol. 32, 2000)

"This book provides an introduction to algebraic dynamical systems and their connection with number theory. This relationship is illustrated by many examples … . I recommend the reading of this interesting book, which may be accessible even for advanced undergraduate students." (Yann Bugeaud, Mathematical Reviews, Issue 2000 e)

"This unusual book is based on a course given to postgraduate students at the University of East Anglia. It could serve as a textbook or as interesting supplementary reading for a course in algebraic dynamics or elliptic curves. … the authors follow the sound pedagogical practice of giving detailed proofs of special cases and providing references to the literature for more general results." (D. W. Boyd, Zentralblatt MATH, Vol. 919, 1999)

"This monograph explores two notions of height in the context of dynamics: Mahler measure and elliptic height. … the material of the book is very well presented and the historical references, examples and exercises make it a useful text for anybody trying to get into the spirit of algebraic dynamical systems." (K. Schmidt, Monatshefte für Mathematik, Issue 3, 1999)

Read More Show Less

Product Details

  • ISBN-13: 9781849968546
  • Publisher: Springer London
  • Publication date: 11/19/2010
  • Series: Universitext Series
  • Edition description: Softcover reprint of hardcover 1st ed. 1999
  • Edition number: 1
  • Pages: 212
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.48 (d)

Table of Contents

1. Lehmer, Mahler and Jensen.- 2. Dynamical Systems.- 3. Mahler’s Measure in Many Variables.- 4. Higher-Dimensional Dynamical Systems.- 5. Elliptic Heights.- 6. The Elliptic Mahler Measure.- A. Algebra.- A.1 Algebraic Integers.- A.2 Integer Matrices.- A.3 Hilbert’s Nullstellensatz.- B. Analysis.- B.1 Stone-Weierstrass Theorem.- B.2 The Gelfand Transform.- C. Division Polynomials.- E.1 Lehmer Primes.- E.2 Elliptic Primes.- F. Exercises and Questions.- F.1 Hints for the Exercises.- F.2 List of Questions.- G. List of Notation.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)