On Exponential Sums Related to the Circle Problem - Slezeviciene, R.; Steading, J. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
Let r(n) count the number of representations of a positive integer n as a sum of two integer squares. We prove a truncated Voronoi-type formula for the twisted Mobius transform _n x r(n) ( 2π ink 4l ), where k and l are positive integers such that k and 4l are coprime, and give some applications (almost periodicity, limit distribution, an asymptotic mean-square formula, and O- and Ω-estimates for the error term).