Equidistribution of Hecke eigenforms on the modular surface
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- by Wenzhi Luo PDF
- Proc. Amer. Math. Soc. 131 (2003), 21-27 Request permission
Abstract:
For the orthonormal basis of Hecke eigenforms in $S_{2k}(\Gamma (1))$, one can associate with it a probability measure $d\mu _{k}$ on the modular surface $X = \Gamma (1) \backslash {\mathbf H}$. We establish that this new measure tends weakly to the invariant measure on $X$ as $k$ tends to infinity, and obtain a sharp estimate for the rate of convergence.References
- W.Luo and P.Sarnak, Mass equidistribution for Hecke eigenforms, preprint, 2001.
- Zeév Rudnick and Peter Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994), no. 1, 195–213. MR 1266075
- D. Zagier, Correction to: “The Eichler-Selberg trace formula on $\textrm {SL}_{2}(\textbf {Z})$” (Introduction to modular forms, Appendix, pp. 44–54, Springer, Berlin, 1976) by S. Lang, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977, pp. 171–173. MR 0480354
Additional Information
- Wenzhi Luo
- Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
- MR Author ID: 260185
- Email: wluo@math.ohio-state.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 21-27
- MSC (2000): Primary 11F11, 11F25
- DOI: https://doi.org/10.1090/S0002-9939-02-06619-4
- MathSciNet review: 1929018