Geodesic
A generalization of the Gauss sum
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 77-80

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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, $0\leq a$, $(a,q)=1$, its value is determined. 
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     author = {H. M. Saliba and V. N. Chubarikov},
     title = {A generalization of the {Gauss} sum},
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H. M. Saliba; V. N. Chubarikov. A generalization of the Gauss sum. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 77-80. http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a17/