ABSTRACT
We mentioned Ramanujan’s sum C ( n,r ) = ∑ h ( mod r ) ( n,r ) = 1 exp ( 2 πihn r ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139463/240bbb93-6815-40d4-a336-935ccad8ea72/content/eq1199.tif"/> while studying the properties of the Euler totient in Chapter IV. C(n, r) and its generalizations are discussed below. It is known that C(n, r) is multiplicative in r and the arithmetical representation of C(n, r) is given by () C(n,r) = ∑ d | (n,r) μ( r d )d https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139463/240bbb93-6815-40d4-a336-935ccad8ea72/content/eq1200.tif"/>
