ABSTRACT
Infinite series expansions of arithmetic functions involving Ramanujan sums https://www.w3.org/1998/Math/MathML"> C ( n , r ) = ∑ h ( mod r ) ( h , r ) = 1 exp ( 2 π i h n r ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq935.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> form an important part of various formulae involving the elementary functions such as d(r), the number of divisors of r and σ(r), the sum of the divisors of r. A criterion for the validity of a Ramanujan expansion of a multiplicative function, due to Richard Warlimont (1983), is presented. Illustrations are shown.
