Abstract:
Results of a numerical experiment on the investigation of the remainder in the problem about the number of integer points in a disk are presented. The pattern of behavior of large deviations of the remainder magnitude from zero is obtained. A numerical confirmation of the hypothesis on the width of maxima according to which all large local maxima of the remainder are fairly wide is obtained, and a hypothetical bound on the remainder magnitude is built. A theorem relating the height (value) of a remainder maximum with the width of this maximum is proved.
Key words:Gauss's circle problem, remainder, relation between the height and width of a maximum, numerical experiment, Landau's formula.