Around the Unit Circle
Language: English
Published by Springer International Publishing, 2021
Series: Book 252 of 261 - Universitext
- Softcover
- New
Seller: moluna, Greven, Germanymoluna
AbeBooks seller since July 9, 2020
Condition: New
£ 56.97
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Add to basketItem description from seller
Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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.
Seller Inventory # 476475146
- Title
- Around the Unit Circle
- Author
- James McKee|Chris Smyth
- Publisher
- Springer International Publishing
- Publication year
- 2021
- Condition
- New
- Binding
- Kartoniert / Broschiert
- Language
- English
- ISBN 10
- 303080030X
- ISBN 13
- 9783030800307
- Dimensions
- 2.5 x 23.5 x 15.5
- Series
- Book 252 of 261: Universitext
- Seller catalogs
- Mathematik/Naturwissenschaften/Technik/Medizin
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.
"Synopsis" may belong to another edition of this title.
About the Author
Chris Smyth, a professorial fellow in Number Theory at the University of Edinburgh, has a long-standing interest in Mahler measure. This dates from his PhD thesis, where he studied Lehmer’s conjecture for nonreciprocal integer polynomials. He discovered the first known closed formula for a 2-dimensional Mahler measure involving an L-function, leading to a deep study of such formulae by Boyd, Deninger, Rodriguez Villegas and others. He invented the explicit auxiliary function method, which applies semi-infinite linear programming to number-theoretic problems, including to the Mahler measure of totally real polynomials.
"About the title" may belong to another edition of this title.
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