Sums of reciprocals of additive functions
running over short intervals
Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 317-326
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\sum _{x \le n \le x+H} 1/f(Q(n))$ and $\sum _{x \le p \le x+H} 1/f(Q(p))$, 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.
Keywords:
letting log where small additive function positive constant obtain estimates quantities sum sum where satisfies certain growth conditions runs prime numbers polynomial integer coefficients whose leading coefficient positive its roots simple
Affiliations des auteurs :
J.-M. De Koninck 1 ; I. Kátai 2
@article{10_4064_cm107_2_11,
author = {J.-M. De Koninck and I. K\'atai},
title = {Sums of reciprocals of additive functions
running over short intervals},
journal = {Colloquium Mathematicum},
pages = {317--326},
publisher = {mathdoc},
volume = {107},
number = {2},
year = {2007},
doi = {10.4064/cm107-2-11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm107-2-11/}
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J.-M. De Koninck; I. Kátai. Sums of reciprocals of additive functions running over short intervals. Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 317-326. doi: 10.4064/cm107-2-11
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