Ternary Kloosterman Sums Modulo 18 Using Stickelberger’s Theorem

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A result due to Helleseth and Zinoviev characterises binary Kloosterman sums modulo 8. We give a similar result for ternary Kloosterman sums modulo 9. This leads to a complete characterisation of values that ternary Kloosterman sums assume modulo 18. The proof uses Stickelberger’s theorem and Fourier analysis.