Distinguishing Gauss sums

Moshe Adrian, Jack Diamond, Kenneth Kramer +1

Let $\F_q$ be the field of order $q=p^f$ for prime $p$. If $G(\chi )$ is the Gauss sum attached to a multiplicative character $\chi$ on $\F_q^\times$, then $G(\chi )=G({\chi }^p)$. We investiga…