A generalization of the Gauss sum / Kh. M. Saliba, V. N. Chubarikov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 2. P. 77-80 [Moscow Univ. Math. Bulletin. Vol. 64, N 2, 2009. P. 92-94].

For the generalized Gauss sum

S(N;a,q)=\sum\limits_{k=1}^{Nq} e\bigg(\frac1N \Big( k-\frac{a}{q}\Big)^2\bigg),

where N,q are natural numbers, a is integer, 0\leq a<q, (a,q)=1, its value is determined.

Key words: Gauss sum, Poisson summation.