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Heights of Polynomials and Entropy...

Heights of Polynomials and Entropy... - 99 edition

Heights of Polynomials and Entropy... - 99 edition

ISBN13: 9781852331252

ISBN10: 1852331259

Heights of Polynomials and Entropy... by Everest - ISBN 9781852331252
Edition: 99
Copyright: 1999
Publisher: Springer-Verlag New York
Published: 1999
International: No
Heights of Polynomials and Entropy... by Everest - ISBN 9781852331252

ISBN13: 9781852331252

ISBN10: 1852331259

Edition: 99

Summary

The main theme of the book is the theory of heights as they appear in various guises. This includes a large body of results on Mahler's measure of the height of a polynomial of which topic there is no book available. The genesis of the measure in a paper by Lehmer is looked at, which is extremely well-timed due to the revival of interest following the work of Boyd and Deninger on special values of Mahler's measure. 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. A large chunk of the book has been devoted to the elliptic Mahler's measure. Special calculation have been included and will be self-contained. One of the most important results about Mahler's measure is that it is the entropy associated to a dynamical system. The authors devote space to discussing this and to giving some convincing and original examples to explain this phenomenon.