Around the Unit Circle Mahler Measure, Integer Matrices and Roots of Unity
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (19...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2021, 2021
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| Edition: | 1st ed. 2021 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1 Mahler Measures of Polynomials in One Variable
- 2 Mahler Measures of Polynomials in Several Variables
- 3 Dobrowolski's Theorem
- 4 The Schinzel–Zassenhaus Conjecture
- 5 Roots of Unity and Cyclotomic Polynomials
- 6 Cyclotomic Integer Symmetric Matrices I: Tools and Statement of the Classification Theorem
- 7 Cyclotomic Integer Symmetric Matrices II: Proof of the Classification Theorem
- 8 The Set of Cassels Heights
- 9 Cyclotomic Integer Symmetric Matrices Embedded in Toroidal and Cylindrical Tesselations
- 10 The Transfinite Diameter and Conjugate Sets of Algebraic Integers
- 11 Restricted Mahler Measure Results
- 12 The Mahler Measure of Nonreciprocal Polynomials
- 13 Minimal Noncyclotomic Integer Symmetric Matrices
- 14 The Method of Explicit Auxiliary Functions
- 15 The Trace Problem For Integer Symmetric Matrices
- 16 Small-Span Integer Symmetric Matrices
- 17 Symmetrizable Matrices I: Introduction
- 18 Symmetrizable Matrices II: Cyclotomic Symmetrizable Integer Matrices
- 19Symmetrizable Matrices III: The Trace Problem
- 20 Salem Numbers from Graphs and Interlacing Quotients
- 21 Minimal Polynomials of Integer Symmetric Matrices
- 22 Breaking Symmetry
- A Algebraic Background
- B Combinatorial Background
- C Tools from the Theory of Functions
- D Tables
- References
- Index