Kai-Man Tsang

On the mean square formula of the error term in the Dirichlet divisor problem

by Preissmann[17]. Further progress towards its size may be hard because, as shown in [11], F (x) = Ω−(x log x). In other words, the room for further improvement is not more than log x. It is anticipated that the omega result is closer to the true magnitude, in virtue of the almost all result in [21]. Very recently, though unable to improve the bound for F (x), Nowak[16] pushed forth the record in a closely analogous situation the circle problem. Let P (t) denote the error term in the circle problem. Owing to the similarity between their Voronoi series, the methodology (based on these series) to handle ∆(t) usually applies to P (t) and vice versa. Let

Moments of the probability density functions of error terms in divisor problems

We derive an explicit formula for the moments of the probability density function of a class of functions. An application of this shows that the density function of the error term in the Pilz divisor problem is asymmetric.