Generalized divisor problem

In 1952 H.E. Richert by means of the theory of Exponents Pairs (developed by J.G. van der Korput and E. Phillips ) improved the above O-term ( see [8] or [4] pag. 221 ). In 1969 E. Kratzel studied the three-dimensional problem. Besides, M.Vogts (1981) and A. Ivic (1981) got some interesting results which generalize the work of P.G. Schmidt of 1968. In 1987 A.Ivic obtained Ω-results for ∫ T 1 ∆ 2 k(a1, . . . , ak, x)dx where ∆k(a1, . . . , ak, x) is the error-term of the summatory function of d(a1, . . . , ak, n). Moreover, he proved that his results hold for the function