Normal numbers and the middle prime factor of an integer

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

Abstrakty

EN

Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 135
• Numer: 1
• Strony: 69-77

Daty

wydano

2014

Twórcy

autor

Jean-Marie De Koninck

• Département de mathématiques et de statistique, Université Laval, Québec, QC G1V 0A6, Canada

autor

Imre Kátai

• Computer Algebra Department, Eötvös Lorand University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/cm135-1-5