ON THE VOLTERRA INTEGRAL EQUATION FOR THE REMAINDER TERM IN THE ASYMPTOTIC FORMULA ON THE ASSOCIATED EULER TOTIENT FUNCTION

Abstract

This paper, first, we consider the Volterra integral equation for the remainder term in the asymptotic formula for the associated Euler totient function. Secondly, we solve the Volterra integral equation and we split the error term in the asymptotic formula for the associated Euler totient function into two summands called arithmetic and analytic part respectively.