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.