Mean-Values of Multiplicative Functions and Natural Boundaries of Power Series with Multiplicative Coefficients

1979 ◽  
Vol s2-19 (1) ◽  
pp. 25-34 ◽  
Author(s):  
L. Lucht ◽  
F. Tuttas
Keyword(s):  
Power Series ◽  
Multiplicative Functions ◽  
Mean Values ◽  
Natural Boundaries

Mean values of some multiplicative functions

2015 ◽  
Vol 97 (1-2) ◽  
pp. 111-123
Author(s):  
A. A. Sedunova
Keyword(s):  
Multiplicative Functions ◽  
Mean Values

scholarly journals Mean values of power series

1968 ◽  
Vol 25 (3) ◽  
pp. 463-494 ◽  
Author(s):  
Thomas Flett
Keyword(s):  
Power Series ◽  
Mean Values

scholarly journals On the asymptotic formulae for some multiplicative functions in short intervals

2015 ◽  
Vol 11 (05) ◽  
pp. 1571-1587 ◽  
Author(s):  
Alisa Sedunova
Keyword(s):  
Short Interval ◽  
Multiplicative Functions ◽  
Density Estimates ◽  
Mean Values ◽  
Short Intervals ◽  
Asymptotic Formulae ◽  
Free Region ◽  
Complex Integration ◽  
The Mean ◽  
Riemann Ζ Function

We are going to study the mean values of some multiplicative functions connected with the divisor function in short interval of summation. The asymptotics for such mean values will be proved. Considering instead of well-known multiplicative functions, their inverses lead to very weak results of application of standard methods of complex integration. In order to get better estimations, we propose another method which uses as its main tools the density estimates and zero-free region for Riemann ζ-function and Dirichlet L-functions.

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