Higher Mahler measure for cyclotomic polynomials and Lehmer's question

الأصل · EN

The k-higher Mahler measure of a nonzero polynomial P is the integral of 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.