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We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic...
An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
Let be the Mahler measure of an algebraic number , and be an open subset of . Then its
is inf , the infimum being over all non-zero non-cyclotomic lying with its conjugates outside . We evaluate when is any annulus centered at . We do the same for a variant of , which we call the transfinite Lehmer constant .Also, we prove the converse to Langevin’s Theorem, which states that if contains a point of modulus . We prove the corresponding result for .
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