Upper bounds on n-dimensional Kloosterman sums

Let pm be any prime power and Kn(a,pm) be the Kloosterman sum , where the xi are restricted to values not divisible by p. Let m,n be positive integers with m 2 and suppose that pγ(n+1). We obtain the upper bound Kn(a,pm) (n+1,p−1)p1/2min(γ,m−2)pmn/2, for odd p. For p=2 we obtain the same bound, with an extra factor of 2 inserted.