2019
Том 71
№ 8

All Issues

Varbanets S. P.

Articles: 2
Article (English)

Generalized Twisted Kloosterman Sum Over [i]

Varbanets S. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 609–618

The twisted Kloosterman sums over Z were studied by V. Bykovsky, A.Vinogradov, N. Kuznetsov, R. W. Bruggeman, R. J. Miatello, I. Pacharoni, A. Knightly, and C. Li. In our paper, we obtain similar estimates for K χ (α, β; γ; q) over [i] and improve the estimates obtained for the sums of this kind with Dirichlet character χ (mod q 1), where q 1 | q.

Article (English)

General Kloosterman sums over ring of Gaussian integers

Varbanets S. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1179-1200

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 $\mathbb{Q}(i)$.