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Experiments on the Lattice Problem of Gauss
1963
Mathematics of Computation
1. Introduction. One of the classical unsolved problems in analytic number theory is concerned with counting the number of lattice points that lie in a circle. If A(r) is the number of lattice points in SD(r) = {(x, y) \x + y ^ r } then the problem is to find the least value of 6 such that (1) E(r) m A{r) -rr2 = 0(r). It has been shown by Loo-Keng Hua [1] that (1) holds for 8 = |f and by G. H. Hardy [2] that it does not hold for 0 = f. A conjecture, frequently attributed to Hardy, asserts that
doi:10.2307/2003839
fatcat:cbzvxric7vc2nfo4yj7ehkzbky