Shifted values of the largest prime factor function and its average value in short intervals

• Autorzy: Jean-Marie De Koninck , Imre Kátai
• Języki publikacji: EN

Abstrakty

EN

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 ≥ 2, we show that if α is an irrational number, then the sequence $(αs_{q}(P(n)))_{n∈ ℕ}$ is uniformly distributed modulo 1.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11K06: General theory of distribution modulo 1

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 1
• Strony: 39-62

Daty

wydano

2016

Twórcy

autor

Jean-Marie De Koninck

• Département de mathématiques et de statistique, UniversitéLaval, Québec G1V 0A6, Canada

autor

Imre Kátai

• Computer Algebra Department, Eötvös Loránd University, Pázmány Péter Sétány I/C, 1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/cm6474-12-2015