The measure of totally positive algebraic integers
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For a totally positive algebraic integer of degree d, we consider the set of values of and the set of values of , where is the length of ¦Á and is the Mahler measure of ¦Á. In this paper, we prove that all except finitely many totally positive algebraic integers ¦Á have and . The computation uses a family of explicit auxiliary functions. We notice that several polynomials with complex roots are used to construct the functions. We also find eight totally positive irreducible polynomials with absolute length greater than 2.364950 and less than 2.37.