On Kloosterman sums over finite fields of characteristic 3

Abstract

Abstract. We study the divisibility by 3 k of Kloosterman sums K(a) over finite fields of characteristic 3. We give a new recurrent algorithm for finding the largest k, such that 3 k divides the Kloosterman sum K(a). This gives a new simple test for zeros of such Kloosterman sums.