On certain values of Kloosterman sums

2009/03/25 by Marko Moisio, Moisio, Marko
Mathematics · #11L05 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0903.4419

openalex publication_date 2009/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K_qⁿ(a) be a Kloosterman sum over the finite field \F_qⁿ of characteristic p. In this note so called subfield conjecture is proved in case p>3: if a≠0 belongs to the proper subfield \F_q of \F_qⁿ, then K_qⁿ(a)≠-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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