Sums of reciprocals of additive functions running over short intervals

J.-M. De Koninck, and I. Kátai. "Sums of reciprocals of additive functions running over short intervals." Colloquium Mathematicae 107.2 (2007): 317-326. <http://eudml.org/doc/284311>.

@article{J2007,
abstract = {Letting f(n) = A log n + t(n), where t(n) is a small additive function and A a positive constant, we obtain estimates for the quantities $∑_\{x≤n≤x+H\} 1/f(Q(n))$ and $∑_\{x≤p≤x+H\} 1/f(Q(p))$, where H = H(x) satisfies certain growth conditions, p runs over prime numbers and Q is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.},
author = {J.-M. De Koninck, I. Kátai},
journal = {Colloquium Mathematicae},
keywords = {additive function},
language = {eng},
number = {2},
pages = {317-326},
title = {Sums of reciprocals of additive functions running over short intervals},
url = {http://eudml.org/doc/284311},
volume = {107},
year = {2007},
}

TY - JOUR
AU - J.-M. De Koninck
AU - I. Kátai
TI - Sums of reciprocals of additive functions running over short intervals
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 2
SP - 317
EP - 326
AB - Letting f(n) = A log n + t(n), where t(n) is a small additive function and A a positive constant, we obtain estimates for the quantities $∑_{x≤n≤x+H} 1/f(Q(n))$ and $∑_{x≤p≤x+H} 1/f(Q(p))$, where H = H(x) satisfies certain growth conditions, p runs over prime numbers and Q is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.
LA - eng
KW - additive function
UR - http://eudml.org/doc/284311
ER -