Geodesic
The mean value of the modulus of a~trigonometric sum
Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1199-1223

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We obtain a simplified upper bound which is uniform in all parameters for the mean value of the modulus of a trigonometric sum. 
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A. A. Karatsuba. The mean value of the modulus of a~trigonometric sum. Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1199-1223. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a0/