On the Values of Kloosterman Sums
Igor E. Shparlinski · IEEE Transactions on Information Theory · 2009
Given a prime p and a positive integer n, we show that the shifted Kloosterman sums SigmaxisinFpnPsi(x + alphaxpn-2)=SigmaxisinF*pnPsi(x+alphax-1)+1, alphaisinF*pn where Psi is a nontrivial additive character of a finite field Fpn of pnelements, do not vanish if alpha belongs to a small subfield Fpm sube Fpn. This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.