On a conjecture of Navarro and Tiep on character fields

In 2021, Navarro and Tiep proposed a conjecture on character fields of finite quasi-simple groups. We develop some theory on sums of roots of unity and use this theory to prove the conjecture for some infinite families of finite quasi-simple groups with known character table. We then use the classification of the irreducible complex characters of the finite general linear groups developed by Green to obtain some partial results about the conjecture for the finite general and special linear groups in arbitrary dimension.