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 , 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.
