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We study fluctuations of the error term for the number of integer latticepoints lying inside a 3-dimensional Cygan-Kor\'anyi ball of large radius. Weprove that the error term, suitably normalized, has a limiting valuedistribution which is absolutely continuous, and we provide estimates for thedecay rate of the corresponding density on the real line. In addition, weestablish the existence of all moments for the normalized error term, and weprove that these are given by the moments of the corresponding density.

Distribution and Moments of the Error Term in the Lattice Point Counting Problem for 3-Dimensional Cygan-Kor\'anyi Balls