Sums of reciprocals of additive functions running over short intervals
Volume 107 / 2007
Colloquium Mathematicum 107 (2007), 317-326
MSC: 11A25, 11N37.
DOI: 10.4064/cm107-2-11
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 $\sum _{x \le n \le x+H} 1/f(Q(n))$ 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.
