Numerical experiments on the Hardy conjecture for the Gauss circle problem

Abstract

The classical unsolved Gauss circle problem concerns estimating the error between the number of lattice points inside a circle and the area of the circle as its radius tends to infinity. About a century ago, Hardy proposed a conjecture concerning this problem. In this paper, we attempt to provide numerical evidence in support of the Hardy conjecture through large-scale numerical computations.

14 pages, 15 figures, 6 FORTRAN programs