Sums of reciprocals of additive functions running over short intervals

• Autorzy: J.-M. De Koninck , I. Kátai
• Języki publikacji: EN

Abstrakty

EN

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 $∑_{x≤n≤x+H} 1/f(Q(n))$ and $∑_{x≤p≤x+H} 1/f(Q(p))$, 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.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11A25: Arithmetic functions; related numbers; inversion formulas

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 2
• Strony: 317-326

Daty

wydano

2007

Twórcy

autor

J.-M. De Koninck

• Département de mathématiques, Université Laval, Québec G1K 7P4, Canada

autor

I. Kátai

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

Identyfikatory

DOI

10.4064/cm107-2-11