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 someinteresting formulae for 2- and 3-higher Mahler measure of cyclotomicpolynomials.
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机译：非零多项式$ P $的$ k $高Mahler度量是单位圆上$ \ log ^ k | P | $的积分。在本说明中，我们考虑Lehmer问题（对于$ k = 1 $是一个长期存在的开放问题），其中$ k> 1 $，并找到了一些有趣的公式，用于关于2和3的马赫量度的环原子多项式。
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