Geodesic
Estimates of remainder terms in the theory of perturbed Dirichlet characters
Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 505-514 Cet article a éte moissonné depuis la source Math-Net.Ru

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Lower and upper estimates for a summatory function of the principal Dirichlet character, perturbed on a finite set of prime numbers, are considered. It is shown that in the case of perturbation on a prime number, the remainder terms in these lower and upper estimates have one and the same order. 
@article{MZM_1978_23_4_a1,
     author = {I. V. Elistratov},
     title = {Estimates of remainder terms in the theory of perturbed {Dirichlet} characters},
     journal = {Matemati\v{c}eskie zametki},
     pages = {505--514},
     year = {1978},
     volume = {23},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a1/}
}
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I. V. Elistratov. Estimates of remainder terms in the theory of perturbed Dirichlet characters. Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 505-514. http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a1/