We obtain several new results contributing to the theory of real equiangular line systems. Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Eu-clidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result,… (More)
A totally real polynomial in Z[x] with zeros α 1 α 2 · · · αn has span αn − α 1. Building on the classification of all characteristic poly-nomials of integer symmetric matrices having span less than 4, we obtain a classification of polynomials having span less than 4 that are the characteristic polynomial of a Hermitian matrix over some quadratic integer… (More)
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least Lehmer's number τ 0 = 1.17628. .. .