Several estimates for the convolution function C[f (x)] := x 1 f (y)f (x/y)(dy/y) and its iterates are obtained when f (x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for T 0 |ζ(1/2 + it)| 2k dt (k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution. 1. Convo...

Sharp versions of some classical results in differential equations are given. Main results consists of a Clunie and a Mohon’ko type theorems, both with sharp forms of error terms. The sharpness of these results is discussed and some applications to nonlinear differential equations are given in the conluding remarks. Moreover, a short introduction on the connection between Nevanlinna theory and ...

In this paper we consider two counting problems associated with compact negatively curved surfaces and improve classical asymptotic estimates due to Margulis. In the first, we show that the number of closed geodesics of length at most T has an exponential error term. In the second we show that the number of geodesic arcs (between two fixed points x and y) of length at most T has an exponential ...

Abstract We derive a new analytic representation of the error function $${\text {erf}}\,\, z$$ erf z in form convergent series whose terms are exponential and rational functions. The expansion holds uniformly z double sector $$\vert \arg (\pm z)\ver...

The objective of this research is to select the appropriate control charts for detecting a shift in the autocorrelated observations. The autocorrelated processes were characterized using AR (1) and IMA (1, 1) for stationary and non-stationary processes respectively. A process model was simulated to achieve the response, the average run length (ARL). The empirical analysis was conducted to quant...

Accepted 4 April 2008 Copyright © EEF ISSN 1399-1183 Species distributional models based on lattice data often display spatial autocorrelation. Spatial autocorrelation means that observations from nearby locations are often more similar than would be expected on a random basis (Legendre and Legendre 1998). Spatial autocorrelation can arise in both species distributions and environmental variabl...