Abstract.
This paper answers a question of Clozel and Ullmo, showing that certain sequences of adelically-defined probability measures defined on an adelic quotient of a solvable group converge to the uniform measure on that quotient. This turns out to depend on any non-trivial estimate for classical Kloosterman sums. At the end, a “horizontal” analogue of the problem is stated and solved using a result of Duke, Friedlander and Iwaniec.
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Received: 30 November 2005
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Kowalski, E. Équirépartition adélique de mesures algébriques dans un groupe résoluble et sommes de Kloosterman. Arch. Math. 88, 220–234 (2007). https://doi.org/10.1007/s00013-006-1818-3
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DOI: https://doi.org/10.1007/s00013-006-1818-3