Abstract
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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