The smallest houses of reciprocal algebraic integers

Abstract

The house of an algebraic integer is the largest modulus of its conjugates. In this work, we compute the minimum of the houses of all reciprocal algebraic integers for degree d ≤ 26. The computations use a large number of explicit auxiliary functions. These functions are related to generalizations of the integer transfinite diameter. They give better bounds than the classical ones for the coefficients of the polynomial with small house.