Hermitean matrices of roots of unity and their characteristic polynomials
Abstract
We investigate spectral conditions on Hermitean matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of $(1\zeta)$, where $\zeta$ is a root of unity. We also prove a generalisation of a classical result of Harary and Schwenk about a relation for traces of powers of a graphadjacency matrix, which is a crucial ingredient for the proofs of our main results.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.05477
 Bibcode:
 2021arXiv210605477G
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 19 pages