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By the collective name of {\it lattice counting} we refer to a setupintroduced in Duke-Rudnick-Sarnak that aim to establish a relationship betweenarithmetic and randomness in the context of affine symmetric spaces. In thispaper we extend the geometric setup from symmetric to real spherical spaces andcontinue to develop the approach with harmonic analysis which was initiated inDuke-Rudnick-Sarnak.

The harmonic analysis of lattice counting on real spherical spaces