Some aspects of higher Mahler measure

We consider the 𝑘-higher Mahler measure 𝑚௞(𝑃) of a Laurent polynomial 𝑃 as the integral of log௞ |𝑃| over the complex unit circle. In this dissertation we derive an explicit formula for the value of ห𝑚௞(𝑃)ห /𝑘! as 𝑘 → ∞. We also derive the rate of convergence of the sequence {𝑚௞(𝑃)/𝑘! }௞ஹଵ for the representative special case 𝑃(𝑧) = 𝑧 + 𝑟 with |𝑟| = 1.