Equidistribution of Hecke eigenforms on the modular surface
Abstract: For the orthonormal basis of Hecke eigenforms in , one can associate with it a probability measure on the modular surface . We establish that this new measure tends weakly to the invariant measure on as tends to infinity, and obtain a sharp estimate for the rate of convergence.
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Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
Keywords: Hecke eigenform, automorphic kernel
Received by editor(s): August 6, 2001
Published electronically: May 8, 2002
Additional Notes: This research was partially supported by NSF grant DMS-9988503, the Alfred P. Sloan Foundation Research Fellowship and the Seed Grant from the Ohio State University
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2002 American Mathematical Society