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## Acta Arithmetica

2000 | 93 | 2 | 117-119
Tytuł artykułu

### A note on evaluations of some exponential sums

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EN
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EN
1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form
$S(a,p^{α}+1) := ∑_{x∈𝔽_q} χ(ax^{p^{α}+1})$
where χ is a non-trivial additive character of the finite field $𝔽_q$, $q = p^e$ odd, and $a ∈ 𝔽*_q$. In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of $p^{α}+1$. The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate certain sums of the form
$∑_{x∈𝔽_q} χ(ax^{p^{α}+1} + bx)$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
117-119
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-08-11
poprawiono
1999-12-30
Twórcy
autor
• Department of Mathematics and Statistics, University of Vaasa, Box 700, 65101 Vaasa, Finland
Bibliografia
• [1] R. S. Coulter, Explicit evaluations of some Weil sums, Acta Arith. 83 (1998), 241-251.
• [2] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Addison-Wesley, Reading, 1983 (now distributed by Cambridge Univ. Press).
• [3] R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer, Dordrecht, 1987.
• [4] M. J. Moisio, On relations between certain exponential sums and multiple Kloosterman sums and some applications to coding theory, preprint, 1997.
• [5] M. J. Moisio, Exponential sums, Gauss sums and cyclic codes, Dissertation, Acta Univ. Oul. A 306, 1998.
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