ON THE IDENTITIES BETWEEN THE ARITHMETIC FUNCTIONS

Abstract

Abstract. Dirichlet series is a Riemann zeta function attachedwith an arithmetic function. Here, we studied the properties ofDirichlet series and found some identities between arithmetic func-tions. 1. IntroductionIn multiplicative analytic number theory, many problems depend onproperties of the zeta function, such as zero free region and zero densityestimates. Thus a better understanding of the zeta function theory isthe simplest of a large class of Dirichlet series which are known as zetafunctions attached with arithmetical functions.A function deflned on the set of natural numbers is called an arith-metic function. There exist many other interesting problems involvingsummatory functions of arithmetical functions, where the generatingseries of the arithmetical functions in question factors into a product.Since these problems give some information of the properties of zerodensity estimates and distribution of primes, several arithmetical func-tions were studied in [2], [3]. In this paper, we study certain relationsbetween arithmetical functions.2. Arithmetical functionsWe list some of mutiplicative arithmetic functions which we will studyin this paper.