Geodesic
Complete rational arithmetic sums
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 60-61

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Let $q>1$ be an integer, $f(x)=a_nx^n+\ldots +a_1x+a_0$ be a polynomial with the integer coefficients, and $(a_n,\ldots ,a_1,q)=1.$ Then is valid the estimation $$\left|S\left(\frac{f(x)}{q}\right)\right|=\left|\sum_{x=1}^q\rho\left(\frac{f(x)}q\right)\right|\ll q^{1-1/n}, $$ where $\rho(t)=0,5-\{t\}.$ 
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     title = {Complete rational arithmetic sums},
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V. N. Chubarikov. Complete rational arithmetic sums. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 60-61. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a10/