An analog of Perron's formula
The author presents a proof of the formula for a mean value of the coefficients of the Dirichlet series with the weight of type \((1- \frac{x}{n})^\alpha\), where \(\alpha>0\) is an arbitrary nonintegral number, and \(\,n\leq x\) is the number of coefficients in the series. The formula is established by means of the method of contour integration.
scientific article; zbMATH DE number 2098933