Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity McKee James
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…
Specifikacia Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity McKee James
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