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We consider the problem of counting the number of rational points of boundedheight in the zero-loci of Brauer group elements on semi-simple algebraicgroups over number fields. We obtain asymptotic formulae for the countingproblem for wonderful compactifications using the spectral theory ofautomorphic forms. Applications include asymptotic formulae for the number ofmatrices over Q whose determinant is a sum of two squares. These resultsprovide a positive answer to some cases of a question of Serre concerning suchcounting problems.

Zero-loci of Brauer group elements on semi-simple algebraic groups