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Abstract
In this paper we study the equidistribution of expanding horospheres in infinite volume geometrically finite rank one locally symmetric manifolds and apply it to the orbital counting problem in an Apollonian sphere packing.
Funding source: NRF
Award Identifier / Grant number: 2010-0024171
The author thanks Pierre Pansu for numerous conversations and his help. He also thanks E. Breuillard for series of lectures about approximate groups, A. Gamburd for the discussions about uniform spectral gap and H. Oh for useful comments about the first draft of this paper. He owes P. Moree much gratitude for his help in number theory in the last section.
Received: 2012-1-7
Revised: 2013-4-17
Published Online: 2013-7-11
Published in Print: 2015-7-1
© 2015 by De Gruyter
