The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3
DOI:
https://doi.org/10.55630/sjc.2011.5.1-14Keywords:
Kloosterman Sums, Divisibility, Exponential SumAbstract
Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.