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

Gary R. W. Greaves, Pavlo Yatsyna

Published 2018-06-21Version 1

For positive integers $e$, we find restrictions modulo $2^e$ on the coefficients of the characteristic polynomial $\chi_S(x)$ of a Seidel matrix $S$. We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\binom{e-2}{2}}$ (resp. $2^{\binom{e-2}{2}+1}$) possibilities for the congruence class of $\chi_S(x)$ modulo $2^e\mathbb Z[x]$. As an application of these results we obtain an improvement to the upper bound for the number of equiangular lines in $\mathbb R^{17}$.