Shifted values of the largest prime factor function and its average value in short intervals

Jean-Marie De Koninck, and Imre Kátai. "Shifted values of the largest prime factor function and its average value in short intervals." Colloquium Mathematicae 143.1 (2016): 39-62. <http://eudml.org/doc/286440>.

@article{Jean2016,
abstract = {We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting $s_\{q\}(n)$ stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence $(αs_\{q\}(P(n)))_\{n∈ ℕ\}$ is uniformly distributed modulo 1.},
author = {Jean-Marie De Koninck, Imre Kátai},
journal = {Colloquium Mathematicae},
keywords = {largest prime factor; shifted prime},
language = {eng},
number = {1},
pages = {39-62},
title = {Shifted values of the largest prime factor function and its average value in short intervals},
url = {http://eudml.org/doc/286440},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Jean-Marie De Koninck
AU - Imre Kátai
TI - Shifted values of the largest prime factor function and its average value in short intervals
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 1
SP - 39
EP - 62
AB - We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting $s_{q}(n)$ stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence $(αs_{q}(P(n)))_{n∈ ℕ}$ is uniformly distributed modulo 1.
LA - eng
KW - largest prime factor; shifted prime
UR - http://eudml.org/doc/286440
ER -