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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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220222b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783030800307 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.9422 |
| Item number |
MCK |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
McKee, James |
| 245 ## - TITLE STATEMENT |
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| Title |
Around the unit circle : Mahler measure, integer matrices and roots of unity |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2021 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xx, 438 p. ; |
| Other physical details |
ill., |
| Dimensions |
24 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
64.99 |
| Price type code |
EUR |
| Unit of pricing |
88.10 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Universitext |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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 Lehmers Problem (1933) and Boyds Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrovs proof of the SchinzelZassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinsons Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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Number Theory |
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Linear Algebra |
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Polynomials |
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Measurement |
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Graph Theory |
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Bogomolov constant |
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| Topical term or geographic name as entry element |
Cassels |
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| Topical term or geographic name as entry element |
Common neighbour class |
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| Topical term or geographic name as entry element |
Conjugate set |
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| Topical term or geographic name as entry element |
Integer symmetric matrix |
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| Topical term or geographic name as entry element |
Dimitrov's Theorem |
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Mahler measure |
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Cyclotomic integers |
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Estes-Guralick Conjecture |
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Fermat's Little Theorem |
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Hardy function |
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Interlacing Theorem |
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Kronecker's Theorem |
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Lehmer's Conjecture |
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Monic polynomial |
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Pisot number |
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Rouche's Theorem |
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Toroidal tessellation |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Smyth, Chris |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |