General Kloosterman sums over ring of Gaussian integers</b>

  • S. P. Varbanets


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 $K(\alpha, \beta; k; \gamma)$ over $\mathbb{Z}[i]$. We also consider the sum $\widetilde{K}(\alpha, \beta; h, q; k)$ 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 $\mathbb{Q}(i)$.
How to Cite
Varbanets, S. P. “General Kloosterman Sums over Ring of Gaussian integers</B&gt;”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 9, Sept. 2007, pp. 1179-00,
Research articles