CONVOLUTION FORMULA AS A STIELTJES RESULTANT

Abstract

In pursuit of the number-theoretic nature of a given set, one defines an arithmetic function and considers its average behavior in view of the fact that independent values are rather singular. We are interested in the asymptotic formula for the summatory function of an arithmetic function which is given as the coefficients of the product of two generating Dirichlet series, i.e. they are convolutions of the respective coefficients. Our main purpose is to elucidate the far-reaching theorem of Lau in the light of the Stieltjes resultant and to give some applications which involve possible logarithmic singularities.