Geodesic
Multiplicative functions on the set of shifted prime numbers
Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1189-1207

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This paper is concerned with the behavior of multiplicative functions on the set $\{p+a\}$, where $p$ is a prime and $a$ is a nonzero integer. Several results are obtained in which either the average value of a multiplicative function on this set is estimated or its asymptotic behavior is determined. As one application a nontrivial estimate of $$\sum\limits_{p\leqslant x}\chi_q(p+a)$$ is found, where $x\geqslant q^{1/4+\varepsilon}$, $q$ is a sufficiently large prime, and $\chi$ is a character of degree greater than 4. 
@article{IM2_1992_39_3_a4,
     author = {N. M. Timofeev},
     title = {Multiplicative functions on the set of shifted prime numbers},
     journal = {Izvestiya. Mathematics },
     pages = {1189--1207},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a4/}
}
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N. M. Timofeev. Multiplicative functions on the set of shifted prime numbers. Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1189-1207. http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a4/