Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 457-464
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M. B. Khripunova. On a multiplicative function on the set of shifted primes. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 457-464. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/
@article{MZM_1998_64_3_a14,
author = {M. B. Khripunova},
title = {On a multiplicative function on the set of shifted primes},
journal = {Matemati\v{c}eskie zametki},
pages = {457--464},
year = {1998},
volume = {64},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/}
}
TY - JOUR
AU - M. B. Khripunova
TI - On a multiplicative function on the set of shifted primes
JO - Matematičeskie zametki
PY - 1998
SP - 457
EP - 464
VL - 64
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/
LA - ru
ID - MZM_1998_64_3_a14
ER -
%0 Journal Article
%A M. B. Khripunova
%T On a multiplicative function on the set of shifted primes
%J Matematičeskie zametki
%D 1998
%P 457-464
%V 64
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/
%G ru
%F MZM_1998_64_3_a14
It is proved that if $f(n)$ is a multiplicative function taking a value $\xi$ on the set of primes such that $\xi^3=1$, $\xi\ne1$ and $f^3(p^r)=1$ for $r\ge2$, then there exists $\theta\in(0,1)$, for which $$ \biggl|\sum_{p\le x}f(p+1)\biggr|\le\theta\pi(x), $$ where $$ \pi(x)=\sum_{p\le x}1. $$
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