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Sums of reciprocals of additive functions running over short intervals

J.-M. De KoninckI. Kátai — 2007

Colloquium Mathematicae

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.

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