Higher Mahler measure for cyclotomic polynomials and Lehmer's question

2011/06/07 by Lalín, Matilde, Sinha, Kaneenika · 1 citation
#11C08 #11R06 #11R09 #11Y35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1106.1304

Abstract

The k-higher Mahler measure of a nonzero polynomial P is the integral of log^k|P| on the unit circle. In this note, we consider Lehmer's question (which is a long-standing open problem for k=1) for k>1 and find some interesting formulae for 2- and 3-higher Mahler measure of cyclotomic polynomials.

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