Application of bounds for trigonometric sums to the problem of divisors and the mean value of the Riemann zeta-function

In this paper we give a new bound for the Riemann zeta-function in the neighborhood of the straight line =1 and indicate its application to the problem of divisors and the mean value of the Riemann zeta-function.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 539–548, November, 1972.The author is grateful to A. F. Lavrik for formulating the problem and for indicating the work of Richert.