On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix

Abstract

For e a positive integer, we find restrictions modulo 2e on the coefficients of the characteristic polynomial χS(x) of a Seidel matrix S. We show that, for a Seidel matrix of order n even (resp., odd), there are at most 2(e−2 2) (resp., 2((e−2 2)+1) possibilities for the congruence class of χS(x) modulo 2eZ[x]. As an application of these results we obtain an improvement to the upper bound for the number of equiangular lines in R17, that is, we reduce the known upper bound from 50 to 49.