Effective equidistribution of the real part of orbits on hyperbolic surfaces
HTML articles powered by AMS MathViewer
- by Jimi L. Truelsen
- Proc. Amer. Math. Soc. 141 (2013), 505-514
- DOI: https://doi.org/10.1090/S0002-9939-2012-11360-7
- Published electronically: June 28, 2012
- PDF | Request permission
Abstract:
For non-cocompact Fuchsian groups with finite covolume we prove that the real part of the orbit of a point in the upper half-plane is equidistributed with an effective error term. This extends previous results by A. Good, M. Risager, and Z. Rudnick. We use the equidistribution result to generalize a theorem by F. Chamizo.References
- Fernando Chamizo, Hyperbolic lattice point problems, Proc. Amer. Math. Soc. 139 (2011), no. 2, 451–459. MR 2736328, DOI 10.1090/S0002-9939-2010-10536-1
- Jean Delsarte, Sur le gitter fuchsien, C. R. Acad. Sci. Paris 214 (1942), 147–179 (French). MR 7769
- P. Erdös and P. Turán, On a problem in the theory of uniform distribution. I, Nederl. Akad. Wetensch., Proc. 51 (1948), 1146–1154 = Indagationes Math. 10, 370–378 (1948). MR 27895
- Anton Good, Local analysis of Selberg’s trace formula, Lecture Notes in Mathematics, vol. 1040, Springer-Verlag, Berlin, 1983. MR 727476, DOI 10.1007/BFb0073074
- Heinz Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959), 1–26 (German). MR 109212, DOI 10.1007/BF01369663
- Heinz Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II, Math. Ann. 142 (1960/61), 385–398 (German). MR 126549, DOI 10.1007/BF01451031
- Heinz Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II, Math. Ann. 143 (1961), 463—464 (German). MR 154980, DOI 10.1007/BF01470758
- A. Gorodnik and A. Nevo. Counting lattice points. J. Reine Angew. Math. 663 (2012), 127-176.
- Henryk Iwaniec, Spectral methods of automorphic forms, 2nd ed., Graduate Studies in Mathematics, vol. 53, American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. MR 1942691, DOI 10.1090/gsm/053
- S. J. Patterson, A lattice-point problem in hyperbolic space, Mathematika 22 (1975), no. 1, 81–88. MR 422160, DOI 10.1112/S0025579300004526
- Morten S. Risager and Zeév Rudnick, On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces, Spectral analysis in geometry and number theory, Contemp. Math., vol. 484, Amer. Math. Soc., Providence, RI, 2009, pp. 187–194. MR 1500148, DOI 10.1090/conm/484/09475
- Morten S. Risager and Jimi L. Truelsen, Distribution of angles in hyperbolic lattices, Q. J. Math. 61 (2010), no. 1, 117–133. MR 2592028, DOI 10.1093/qmath/han033
Bibliographic Information
- Jimi L. Truelsen
- Affiliation: Department of Mathematical Sciences, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
- Email: lee@imf.au.dk
- Received by editor(s): June 18, 2011
- Received by editor(s) in revised form: July 9, 2011
- Published electronically: June 28, 2012
- Additional Notes: The author was funded by a stipend from The Danish Agency for Science, Technology and Innovation.
- Communicated by: Kathrin Bringmann
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 505-514
- MSC (2010): Primary 11B05, 11J71; Secondary 11M36
- DOI: https://doi.org/10.1090/S0002-9939-2012-11360-7
- MathSciNet review: 2996954