Geodesic
Shifted values of the largest prime factor function and its average value in short intervals
Jean-Marie De Koninck1 ; Imre Kátai2
1 Département de mathématiques et de statistique UniversitéLaval Québec G1V 0A6, Canada
2 Computer Algebra Department Eötvös Loránd University Pázmány Péter Sétány I/C 1117 Budapest, Hungary
Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 39-62.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $s_q(n)$ stand for the sum of the digits of $n$ in base $q\ge 2$, we show that if $\alpha $ is an irrational number, then the sequence $(\alpha s_q(P(n)))_{n\in \mathbb {N}}$ is uniformly distributed modulo 1.
DOI : 10.4064/cm6474-12-2015
Keywords: obtain estimates average value largest prime factor short intervals where complex valued additive function multiplicative function satisfying certain conditions letting stand sum digits base alpha irrational number sequence alpha n mathbb uniformly distributed modulo nbsp

Jean-Marie De Koninck 1 ; Imre Kátai 2

1 Département de mathématiques et de statistique UniversitéLaval Québec G1V 0A6, Canada
2 Computer Algebra Department Eötvös Loránd University Pázmány Péter Sétány I/C 1117 Budapest, Hungary 
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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 Mathematicum, Tome 143 (2016) no. 1, pp. 39-62. doi : 10.4064/cm6474-12-2015. http://geodesic.mathdoc.fr/articles/10.4064/cm6474-12-2015/

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