Heights of Polynomials and Entropy in Algebraic Dynamics

Graham Everest, Thomas Ward

212 pages, parution le 01/07/1999

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Résumé

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.

Contents

1 Lehmer, Mahler and Jensen 1
2 Dynamical Systems 29
3 Mahler's Measure in Many Variables 51
4 Higher-Dimensional Dynamical Systems 81
5 Elliptic Heights 91
6 The Elliptic Mahler Measure 117

A Algebra 145
B Analysis 151
C Division Polynomials 157
D Proof of Mahler's Bound for m(F') 159
E Calculations on [Delta][subscript n](F) and E[subscript n](F) 165
F Exercises and Questions 169
G List of Notation 197

Bibliography 199
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Graham Everest, Thomas Ward
Parution	01/07/1999
Nb. de pages	212
Format	16 x 24
Couverture	Relié
Poids	446g
Intérieur	Noir et Blanc
EAN13	9781852331252
ISBN13	978-1-85233-125-2