Abstract
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bernstein J., Reznikov A., Analytic continuation of representations and estimates of automorphic forms, Ann. of Math., 1999, 150(1), 329–352
Bernstein J., Reznikov A., Estimates of automorphic functions, Mosc. Math. J., 2004, 4(1), 19–37
Deitmar A., Invariant triple products, Int. J. Math. Math. Sci., 2006, #48274
Gangolli R., Varadarajan V.S., Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb., 101, Springer, Berlin, 1988
Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products, 7th ed., Elsevier/Academic Press, Amsterdam, 2007
Harish-Chandra, Harmonic analysis on real reductive groups. I. The theory of the constant term, J. Functional Analysis, 1975, 19, 104–204
Iwaniec H., Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math., 53, American Mathematical Society, Providence, 2002
Knapp A.W., Representation Theory of Semisimple Groups, Princeton Landmarks Math., Princeton University Press, Princeton, 2001
Molčanov V.F., Tensor products of unitary representations of the three-dimensional Lorentz group, Izv. Akad. Nauk SSSR Ser. Mat., 1979, 43(4), 860–891 (in Russian)
Seeger A., Sogge C.D., Bounds for eigenfunctions of differential operators, Indiana Univ. Math. J., 1989, 38(3), 669–682
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Deitmar, A. Fourier expansion along geodesics on Riemann surfaces. centr.eur.j.math. 12, 559–573 (2014). https://doi.org/10.2478/s11533-013-0366-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-013-0366-x