Analytic properties of the error term arising from the arithmetical problems

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First we studied the analytic properties of the Dirichlet series obtained by the arithmetical error term, especially by the error termΔ(x) arising from the Dirichlet divisor problems. We also derived the explicit formula of the integral involvingΔ(x). Secondly we treated the sum of Chowla and Walum. We succeeded to improve its upper bound by using the theory of exponent pairs. We also got an improvement of its mean square formula. As a generalization of our study, we considered closely the difference of the discrete and continuous mean square formulas of the error term obtained from the general divisor problems by using the generalized sum of Chowla and Walum.