Abstract
Quasi-Frobenius (QF) rings comprise finite fields, Galois rings and enjoy remarkable character-theoretic properties. We define two types of Gauss sums over QF rings: complete and incomplete. We compute the modulus of the former. We estimate the modulus of the latter from above and give an application to Gauss sums over Galois rings. We derive the analogue of Stickelberger theorem for Gauss sums indexed by the Teichmuller set.
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