THE NUMBER OF LATTICE POINTS BELOW A LOGARITHMIC CURVE

For arbitrary real b > 1 and for a large real parameter t let R(b, t) be the number of lattice points between the curve b(y) = x (1 less tha n or equal to x less than or equal to t) and the x-axis, the points on the x-ards being counted with the factor 1/2. Furthermore, let the la ttice rest Gamma(b, t) be defined as the difference between R(b, t) an d the area of the domain. The asymptotic behaviour of Gamma(b, t) for t --> infinity and also for b --> 1(+) are investigated.