Geodesic
Sums of values of nonprincipal characters over a sequence of shifted primes
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 234-260

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For a nonprincipal character $\chi $ modulo $D$, we prove a nontrivial estimate of the form $\sum _{n\le x}\Lambda (n)\chi (n-l)\ll x\exp \{-0.6\sqrt {\ln D}\}$ for the sum of values of $\chi $ over a sequence of shifted primes in the case when $x\ge D^{1/2+\varepsilon }$, $(l,D)=1$, and the modulus of the primitive character generated by $\chi $ is a cube-free number.
Keywords: Dirichlet character, shifted primes, short character sum, exponential sum over primes. 
@article{TM_2017_299_a14,
     author = {Z. Kh. Rakhmonov},
     title = {Sums of values of nonprincipal characters over a sequence of shifted primes},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {234--260},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_299_a14/}
}
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Z. Kh. Rakhmonov. Sums of values of nonprincipal characters over a sequence of shifted primes. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 234-260. http://geodesic.mathdoc.fr/item/TM_2017_299_a14/