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Description of  Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity (Universitext)

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. Read more