Gauss Sums over Quasi-Frobenius Rings

Philippe Langevin () and Patrick Solé ()
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Philippe Langevin: Université de Toulon et du Var, Groupe d’Etudé de Codage de Toulon
Patrick Solé: CNRS-13S, ESSI

A chapter in Finite Fields and Applications, 2001, pp 329-340 from Springer

Abstract: 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 Teichmüller set.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56755-1_26

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DOI: 10.1007/978-3-642-56755-1_26

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