Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula

Faruk Gologlu; Gary McGuire; Richard Moloney

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arXiv · 1005.4548

Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula

Faruk Gologlu·Gary McGuire·Richard Moloney

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Abstract

Let $\mathcal{K}(a)$ denote the Kloosterman sum on the finite field of order $2^n$. We give a simple characterization of $\mathcal{K}(a)$ modulo 16, in terms of the trace of $a$ and one other function. We also give a characterization of $\mathcal{K}(a)$ modulo 64 in terms of a different function, which we call the lifted trace. Our proofs use Fourier analysis, Stickelberger's theorem and the Gross-Koblitz formula.

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Faruk Gologlu, Gary McGuire, Richard Moloney. 2010-05-28. Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula. https://arxiv.org/abs/1005.4548

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