The rate of growth of moments of certain cotangent sums

We consider cotangent sums associated to the zeros of the Estermann zeta function considered by the authors in their previous paper (Maier and Rassias, Generalizations of a cotangent sum associated to the Estermann zeta function, 2014). We settle a question on the rate of growth of the moments of these cotangent sums left open in Maier and Rassias (Generalizations of a cotangent sum associated to the Estermann zeta function, 2014), and obtain a simpler proof of the equidistribution of these sums.