On the Distribution of a Cotangent Sum

Maier and Rassias computed the moments and proved a distribution result for the cotangent sum c(0)(a/q) := -Sigma(m<q) m/q cot(pi ma/q) on average over 1/2 < A(0) <= a/q < A(1) < 1, as q -> 8. We give a simple argument that recovers their results (with stronger error terms) and extends them to the full range 1 <= a < q. Moreover, we give a density result for c(0) and answer a question posed by Maier and Rassias on the growth of the moments of c(0).