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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crescendo

Cyclotomic Integer Symmetric Matrices I: Tools and Statement of the Classification Theorem,e define the Mahler measure of . to be .. This Mahler measure is a function of the eigenvalues of .. If . is symmetric, then we get more control on its eigenvalues and hence on its Mahler measure. We start on the task of finding integer symmetric matrices that have small Mahler measure. Most of thes

Exposure

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.

Libido

The Transfinite Diameter and Conjugate Sets of Algebraic Integers,o consideration of which such sets contain finitely or infinitely many sets of conjugate algebraic integers. We also summarise the main results concerning two variants of the transfinite diameter, namely the integer transfinite diameter and the monic integer transfinite diameter.

Cacophonous

令人心醉

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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https://doi.org/10.1007/978-981-16-4404-7for symmetrizable matrices. We explore connections with equitable partitions of signed graphs. It will transpire that symmetrizable integer matrices are precisely those that occur as quotient matrices for these equitable partitions.

嫌惡

Symmetrizable Matrices I: Introduction,for symmetrizable matrices. We explore connections with equitable partitions of signed graphs. It will transpire that symmetrizable integer matrices are precisely those that occur as quotient matrices for these equitable partitions.