Geodesic
Evaluation of character sums over the continuous interval of summation
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 118-122.

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In this paper we prove several theorems. Theorem 1, to assess the character sums over the continuous interval based on the use of the formula A. Postnikov and Theorem 2, for the right choice of parameters, estimates of this kind.
Keywords: A Prime number, the sum of Dirichlet characters, simple modules, continuous period of summation, nonprincipal character estimate of amounts formula A. G. Postnikova, short amount of characters, the exponential decrease, trigonometric sum. 
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A. A. Kopaneva; E. A. Burlakova. Evaluation of character sums over the continuous interval of summation. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 118-122. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a9/

[1] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, 2-e izd., Nauka, M., 1983, 240 pp. | MR

[2] Postnikov A. G., Izbrannye trudy, ed. V. N. Chubarikov, Fizmatlit, M., 2005, 512 pp. | MR | Zbl