General Kloosterman sums over ring of Gaussian integers
Abstract
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 $\mathbb{Q}(i)$.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 9, pp 361-378.
Citation Example: Varbanets S. P. General Kloosterman sums over ring of Gaussian integers // Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1179-1200.
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