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Titlebook: Around the Unit Circle; Mahler Measure, Inte James McKee,Chris Smyth Textbook 2021 Springer Nature Switzerland AG 2021 Mahler measure.Lehme

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Exploring the Translatability of Emotions(those that have Mahler measure 1), we introduce the tool of representing the matrices by Gram vectors; finally, we state classification of integer symmetric matrices that have Mahler measure 1 (proof in the next chapter).
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https://doi.org/10.1007/978-3-030-91748-7t of the chapter is devoted to the discussion of some problems and conjectures about cyclotomic integers due to R. M. Robinson. Finally, there are some results on multiplicative relations between conjugate roots of unity.
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Textbook 2021tic 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–Zasse
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Cyclotomic Integer Symmetric Matrices II: Proof of the Classification Theorem,cted charged signed graphs. The uncharged case (signed graphs) is considered first, and then the complications of adding charges are resolved, before gluing all the work together to complete the classification.
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The Trace Problem for Integer Symmetric Matrices,n formulate an analogous problem for the mean traces of positive definite integer symmetric matrices. As with Lehmer’s Conjecture, we find that the restricted combinatorial problem is more tractable, and indeed, we can solve it. We also develop a structure theory for minimal-trace examples.
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Around the Unit Circle978-3-030-80031-4Series ISSN 0172-5939 Series E-ISSN 2191-6675
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