3 citations · 5 across the 5 of their papers we have counts for
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On totally real numbers and equidistribution
Paul Fili, Zachary Miner
C.J. Smyth and later Flammang studied the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of th…
Equidistribution and the heights of totally real and totally p-adic numbers
Paul Fili, Zachary Miner
C.J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of…
A generalization of Dirichlet's unit theorem
Paul Fili, Zachary Miner
We generalize Dirichlet's -unit theorem from the usual group of -units of a number field to the infinite rank group of all algebraic numbers having nontrivial valuations…
Norms extremal with respect to the Mahler measure
Paul Fili, Zachary Miner
In a previous paper, the authors introduced several vector space norms on the space of algebraic numbers modulo torsion which corresponded to the Mahler measure on a certain class…
Orthogonal decomposition of the space of algebraic numbers and Lehmer's problem
Paul Fili, Zachary Miner
We introduce vector space norms associated to the Mahler measure by using the L^p norm versions of the Weil height recently introduced by Allcock and Vaaler. In order to do this, w…