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Mat. Zametki, 2015, Volume 97, Issue 1, Pages 115–128 (Mi mz10571)  

Mean Values of Some Multiplicative Functions

A. A. Sedunova

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We obtain asymptotic formulas for the mean values of a number of arithmetic functions $f=f(n)$ on a “short” interval of the form $x<n\le x+h$, where the length $h$ differs from $x$ by a power-law decrease: $h=x^{1-\delta}$, $0<\delta<1$.

Keywords: arithmetic function, mean value of a multiplicative function, Riemann zeta function, Dirichlet series.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-31165_мол_а
This work was supported by the Russian Foundation for Basic Research (grant no. 12-01-31165_mol_a).


DOI: https://doi.org/10.4213/mzm10571

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English version:
Mathematical Notes, 2015, 97:1, 111–123

Bibliographic databases:

Document Type: Article
UDC: 511
Received: 27.05.2013
Revised: 07.04.2014

Citation: A. A. Sedunova, “Mean Values of Some Multiplicative Functions”, Mat. Zametki, 97:1 (2015), 115–128; Math. Notes, 97:1 (2015), 111–123

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