We estimate the error term in the Ingham Tauberian theorem. This estimation of the error term is accomplished by considering an elementary proof of a weak form of Wiener's general Tauberian theorem and by using a zero-free region for the Riemann zeta function. 1. Introduction. As an important application of his general Tauberian theorem (GTT), in 1932, Wiener [6] gave a new proof of the prime n...

In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts finite type. We deal with two classes such systems: attracting and parabolic. The latter being treated means former. prove fairly complete asymptotic counting results for multipliers diameters associated preimages or periodic orbits ordered a natural geometr...

After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted meanmethods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence ...