Geodesic
The mean value for Weyl sum over the ring of algebraic integers
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 113-117.

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The estimates of the mean value trigonometrical Weyl sum in a rational number field are given in the paper [1] of Arkhipov G. I. The estimates of the mean value trigonometrical sum in real algebraic numbers is found in the present article.
Keywords: the mean value theorem, trigonometrical sums. 
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A. V. Kokorev. The mean value for Weyl sum over the ring of algebraic integers. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 113-117. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a8/

[1] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987

[2] Kokorev A. V., “Teorema o srednem znachenii trigonometricheskikh summ v pole algebraicheskikh chisel 2 stepeni”, Uchenye zapiski Orlovskogo gos. un-ta, 2012, no. 3(47), 29–38