Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity (Universitext) - Softcover
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- VerlagSpringer
- Erscheinungsdatum2021
- ISBN 10 303080030X
- ISBN 13 9783030800307
- EinbandTapa blanda
- Auflage1
- Anzahl der Seiten460
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Around the Unit Circle : Mahler Measure, Integer Matrices and Roots of Unity
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Springer International Publishing 2021-12-09, Berlin
(2021)
ISBN 10: 303080030X
ISBN 13: 9783030800307
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Buchbeschreibung paperback. Zustand: New. Language: ENG. Artikel-Nr. 9783030800307
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Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity (Universitext)
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Buchbeschreibung Paperback. Zustand: New. BRAND NEW ** SUPER FAST SHIPPING FROM UK WAREHOUSE ** 30 DAY MONEY BACK GUARANTEE. Artikel-Nr. 9783030800307-GDR
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Around the Unit Circle : Mahler Measure, Integer Matrices and Roots of Unity
Verlag:
Springer International Publishing
(2021)
ISBN 10: 303080030X
ISBN 13: 9783030800307
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov's proof of the Schinzel-Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson's 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 setsof 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. Artikel-Nr. 9783030800307
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Around the Unit Circle
Verlag:
Springer International Publishing
(2021)
ISBN 10: 303080030X
ISBN 13: 9783030800307
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Buchbeschreibung Kartoniert / Broschiert. Zustand: New. A thorough introduction to the combinatorial approach to Mahler measure and morePresents results that have not previously appeared in book formIncludes new tables of small Mahler measures and limit pointsAppendices on prerequisites m. Artikel-Nr. 476475146
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