On the Values of Kloosterman Sums
Given a prime p and a positive integer n, we show that the shifted Kloosterman sums Sigma (x is an element of Fpn) psi (x + ax(pn-2)) = Sigma (x is an element of F+pn) psi(x + ax(-1)) + 1, a is an element of F(pn)* where psi is a nontrivial additive character of a finite field F(pn) of p(n) elements, do not vanish if a belongs to a small sublield F(pm) subset of F(pn). This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.
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