Local Density Conjecture for Salem numbers

Let T{\rm T} be the set of Salem numbers, let c>1c>1, and let AqA_q denote the classes of Salem numbers used in the source. Local Density Conjecture. For every c>1c>1, there exists M>0M>0 such that

T[1,c]2qMAq.{\rm T}\cap[1,c]\subseteq\bigcup_{2\leq q\leq M}A_q.

The conjecture concerns the distribution of Salem numbers among the classes AqA_q; the source states that their distribution in the other classes remains obscure.

Sources & referencesView supporting material

Primary source

Christelle Guichard and Jean-Louis Verger-Gaugry, “On Salem numbers, expansive polynomials and Stieltjes continued fractions”, arXiv:1402.6681 (2015).

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