Science and Education Publishing Turkish Journal of Analysis and Number Theory 2 3 2014 07 14 On the Moments of the Function E*(t) 102 109 EN Aleksandar Ivi? Aleksandar Ivi?, Katedra Matematike RGF-A, Universitet U Beogradu, Du?ina, Beograd, Serbia TJANT2014239 10.12691/tjant-2-3-9 2014 06 19 2014 07 02 2014 07 14 Let denote the error term in the Dirichlet divisor problem, and the error term in the asymptotic formula for the mean square of If with then we discuss bounds for third, fourth and fifth power moment of We also prove that always changes sign in for and obtain (conditionally) the existence of its large positive, or small negative values.