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Gauss Sums over Quasi-Frobenius Rings

In: Finite Fields and Applications

Author

Listed:
  • Philippe Langevin

    (Université de Toulon et du Var, Groupe d’Etudé de Codage de Toulon)

  • Patrick Solé

    (CNRS-13S, ESSI)

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.

Suggested Citation

  • Philippe Langevin & Patrick Solé, 2001. "Gauss Sums over Quasi-Frobenius Rings," Springer Books, in: Dieter Jungnickel & Harald Niederreiter (ed.), Finite Fields and Applications, pages 329-340, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56755-1_26
    DOI: 10.1007/978-3-642-56755-1_26
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