Abstract: In 2008, Pritsker introduced an areal analog of the Mahler measure, where the integral is over the closed unit disc instead of the unit circle. One of the interesting properties of Pritsker's measure is that the statement of Lehmer's conjecture for it fails. Using the framework of adelic heights introduced by Favre and Rivera-Letelier, we will construct a height analog of Pritsker's measure, determined by a finite set of places for a fixed number field. After defining this height, we examine its basic properties. We then show that for any choice of a finite set of places of $\mathbb{Q}$, the analogous statement of Lehmer's conjecture for our height fails.
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