General Kloosterman sums over ring of Gaussian integers - Varbanets, S. P. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
The general Kloosterman sum $K(m, n; k; q)$ over $\mathbb{Z}$ was studied by $S$. Kanemitsu, Y. Tanigawa, Yi. Yuan, Zhang Wenpeng in their research of problem of D. H. Lehmer. In this paper, we obtain the similar estimations of $K(α, β; k; γ)$ over $\mathbb{Z}[i]$. We also consider the sum $\widetilde{K}(α, β; h, q; k)$ which has not an analogue in the ring $\mathbb{Z}$ but it can be used for the inversigation of the second moment of the Hecke zeta-fonction of field $\mathbb{Q}(i)$.