A note on evaluations of some exponential sums
Marko J. Moisio
Acta Arithmetica, Tome 92 (2000), p. 117-119 / Harvested from The Polish Digital Mathematics Library
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1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form S(a,pα+1):=∑x∈qχ(axpα+1) where χ is a non-trivial additive character of the finite field q, q=pe odd, and a∈*q. In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of pα+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∈qχ(axpα+1+bx).

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207403 
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Marko J. Moisio. A note on evaluations of some exponential sums. Acta Arithmetica, Tome 92 (2000) pp. 117-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav93i2p117bwm/

[00000] [1] R. S. Coulter, Explicit evaluations of some Weil sums, Acta Arith. 83 (1998), 241-251. | Zbl 0924.11098

[00001] [2] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Addison-Wesley, Reading, 1983 (now distributed by Cambridge Univ. Press). | Zbl 0554.12010

[00002] [3] R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer, Dordrecht, 1987. | Zbl 0662.94014

[00003] [4] M. J. Moisio, On relations between certain exponential sums and multiple Kloosterman sums and some applications to coding theory, preprint, 1997.

[00004] [5] M. J. Moisio, Exponential sums, Gauss sums and cyclic codes, Dissertation, Acta Univ. Oul. A 306, 1998. | Zbl 0970.94011