The circle and devisor problem

New proofs for the classical bounds P(x) ? x1/3, ?(x) ? h1/3 log x are given. Here P(x) denotes the error term in the classical circle, and ? (x) in the classical divisor problem. .

A Divisor Problem for Values of Polynomials

In this article we investigate the average order of the arithmetical functionwhere p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.