On certain values of Kloosterman sums

Marko Moisio

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arXiv · 0903.4419

On certain values of Kloosterman sums

Marko Moisio

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Abstract

Let $K_{q^n}(a)$ be a Kloosterman sum over the finite field $\F_{q^n}$ of characteristic $p$. In this note so called subfield conjecture is proved in case $p>3$: if $a\ne0$ belongs to the proper subfield $\F_q$ of $\F_{q^n}$, then $K_{q^n}(a)\ne-1$. This completes recent works on the subfield conjecture by Shparlinski, and Moisio and Lisonek. The problem is motivated by some applications to bent functions. Moreover, in the course of the proof a large class of translates of Dickson polynomials are shown to be irreducible.

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Marko Moisio. 2009-04-16. On certain values of Kloosterman sums. https://arxiv.org/abs/0903.4419

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