Abstract
Let p be a prime and q = p s and ζk a fixed primitive kth root of unity in some extension of Q. Let χ be a multiplicative character over Fq of order k and J (χ, χ) the associated Jacobi sum. We give examples of χ which satisfy J (χ, χ) ∈p [s/2]Z[ζk]. Moreover, for s = 3, we prove that there is only a finite number of k such that J(χ, χ) is an element of pZ[ζk] except for the case where k is divisible by nine and p ≡1 ± k/3 (mod k).
