Shifted values of the largest prime factor function and its average value in short intervals
Jean-Marie De Koninck ; Imre Kátai
Colloquium Mathematicae, Tome 144 (2016), p. 39-62 / Harvested from The Polish Digital Mathematics Library
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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting sq(n) stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence (αsq(P(n)))n∈ℕ is uniformly distributed modulo 1.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:286440 
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Jean-Marie De Koninck; Imre Kátai. Shifted values of the largest prime factor function and its average value in short intervals. Colloquium Mathematicae, Tome 144 (2016) pp. 39-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6474-12-2015/