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Cover: 9781852331252 | Heights of Polynomials and Entropy in Algebraic Dynamics | Buch | xii
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Heights of Polynomials and Entropy in Algebraic Dynamics
Buch von Thomas Ward (u. a.)
Sprache: Englisch

46,95 €*

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Lieferzeit 1-2 Wochen

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Beschreibung
Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of­ fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in­ tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome­ try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con­ nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi­ als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.
Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of­ fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in­ tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome­ try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con­ nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi­ als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.
Zusammenfassung

Uncovers new and interesting connections between number theory and dynamics -

The book covers many results of Mahler's measure of the height of a polynomial.

A book has never before been published covering this topic - The early parts of the book are based on lectures given to post- graduates (at several levels) at UEA during semester 2 of the year 1997/98

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1999
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xii
212 S.
ISBN-13: 9781852331252
ISBN-10: 1852331259
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Ward, Thomas
Everest, Graham
Hersteller: Springer London
Springer-Verlag London Ltd.
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 17 mm
Von/Mit: Thomas Ward (u. a.)
Erscheinungsdatum: 12.02.1999
Gewicht: 0,512 kg
Artikel-ID: 106693901
Zusammenfassung

Uncovers new and interesting connections between number theory and dynamics -

The book covers many results of Mahler's measure of the height of a polynomial.

A book has never before been published covering this topic - The early parts of the book are based on lectures given to post- graduates (at several levels) at UEA during semester 2 of the year 1997/98

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1999
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xii
212 S.
ISBN-13: 9781852331252
ISBN-10: 1852331259
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Ward, Thomas
Everest, Graham
Hersteller: Springer London
Springer-Verlag London Ltd.
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 17 mm
Von/Mit: Thomas Ward (u. a.)
Erscheinungsdatum: 12.02.1999
Gewicht: 0,512 kg
Artikel-ID: 106693901
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