Distribution of values of Dirichlet characters in the sequence of shifted primes
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 113-117.

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The new estimate for the sum of the values of a primitive Dirichlet character modulo an integer $q$ has been obtained over the sequence of shifted primes $p-l$, $(l,q)=1$, $p\le x$. This estimate is nontrivial for $x\ge q^{\frac56+\varepsilon}$ and refines the estimate obtained by J. B. Friedlander, K. Gong, I. E. Shparlinskii. Their estimate holds provided that $x\ge q^{8/9+\varepsilon}$.
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Z. Kh. Rakhmonov. Distribution of values of Dirichlet characters in the sequence of shifted primes. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 113-117. http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a18/

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