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 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 Z[i]. We also consider the sum K(α, β; h, q; k) which has not an analogue in the ring Z but it can be used for the inversigation of the second moment of the Hecke zeta-fonction of field Q(i).