Sums of reciprocals of additive functions running over short intervals

J.-M. De Koninck; I. Kátai

Colloquium Mathematicae, Tome 107 (2007), p. 317-326 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $\sum_{x \leq n \leq x + H} 1 / f (Q (n))$ and $\sum_{x \leq p \leq x + H} 1 / f (Q (p))$ , 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.

Publié le : 2007-01-01

Zbl 1219.11142

EUDML-ID : urn:eudml:doc:284311

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J.-M. De Koninck; I. Kátai. Sums of reciprocals of additive functions running over short intervals. Colloquium Mathematicae, Tome 107 (2007) pp. 317-326. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-11/