Some congruences of Kloosterman sums and their characteristic polynomials

TextWe prove two congruence results concerning Kloosterman sums over finite fields. The first result concerns the coefficients of the characteristic polynomial over QQ of a Kloosterman sum, and the second result gives a characterisation of ternary Kloosterman sums modulo 27. We use methods from algebraic number theory such as Stickelbergerʼs theorem and the Gross–Koblitz formula, as well as Fourier analysis.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=VJcB6W_PQ0s.