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Archiv der Mathematik

, Volume 88, Issue 3, pp 220–234 | Cite as

Équirépartition adélique de mesures algébriques dans un groupe résoluble et sommes de Kloosterman

  • E. Kowalski
Article
  • 40 Downloads

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.

Mathematics Subject Classification (2000).

20G35 11L05 

Keywords.

Equidistribution Kloosterman sums roots of quadratic congruences 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Université Bordeaux I - A2XTalence CedexFrance

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