The hyperbolic lattice point problem in conjugacy classes

References

[1] Bruin P., Explicit bounds on automorphic and canonical Green functions of Fuchsian groups, Mathematika 60 (2014), no. 2, 257–306. 10.1112/S0025579314000060Search in Google Scholar

[2] Chamizo F., Topics in analytic number theory, Ph.D. thesis, Universdad Autónoma de Madrid, 1994. Search in Google Scholar

[3] Chamizo F., Some applications of the large sieve in Riemann surfaces, Acta Arith. 77 (1996), no. 4, 315–337. 10.4064/aa-77-4-315-337Search in Google Scholar

[4] Chamizo F., The large sieve in Riemann surfaces, Acta Arith. 77 (1996), no. 4, 303–313. 10.4064/aa-77-4-303-313Search in Google Scholar

[5] Duke W., Rudnick Z. and Sarnak P., Density of integer points on affine homogeneous varieties, Duke Math. J. 71 (1993), no. 1, 143–179. 10.1215/S0012-7094-93-07107-4Search in Google Scholar

[6] Erdélyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher Transcendental Functions, Volume I, McGraw–Hill, New York, 1953. Search in Google Scholar

[7] Eskin A. and McMullen C., Mixing, counting, and equidistribution in Lie groups, Duke Math. J. 71 (1993), no. 1, 181–209. 10.1215/S0012-7094-93-07108-6Search in Google Scholar

[8] Fay J. D., Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math. 293/294 (1997), 143–203. Search in Google Scholar

[9] Garbin D., Jorgenson J. and Munn M., On the appearance of Eisenstein series through degeneration, Comment. Math. Helv. 83 (2008), no. 4, 701–721. 10.4171/CMH/140Search in Google Scholar

[10] Good A., Local Analysis of Selberg’s Trace Formula, Lecture Notes in Math. 1040, Springer, Berlin, 1983. 10.1007/BFb0073074Search in Google Scholar

[11] Gradshteyn I. S. and Ryzhik I. M., Table of Integrals, Series, and Products, 7th ed., Academic Press, Amsterdam, 2007. Search in Google Scholar

[12] Günther P., Gitterpunktprobleme in symmetrischen Riemannschen Räumen vom Rang 1, Math. Nachr. 94 (1980), 5–27. 10.1002/mana.19800940102Search in Google Scholar

[13] Hill R. and Parnovski L., The variance of the hyperbolic lattice point counting function, Russ. J. Math. Phys. 12 (2005), no. 4, 472–482. Search in Google Scholar

[14] Huber H., Über eine neue Klasse automorpher Funktionen und ein Gitterpunktproblem in der hyperbolischen Ebene. I, Comment. Math. Helv. 30 (1956), 20–62. 10.1007/BF02564331Search in Google Scholar

[15] Huber H., Ein Gitterpunktproblem in der hyperbolischen Ebene, J. Reine Angew. Math. 496 (1998), 15–53. 10.1515/crll.1998.027Search in Google Scholar

[16] Iwaniec H., Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math. 53, American Mathematical Society, Providence, 2002. 10.1090/gsm/053/05Search in Google Scholar

[17] Martin K., McKee M. and Wambach E., A relative trace formula for a compact Riemann surface, Int. J. Number Theory 7 (2011), no. 2, 389–429. 10.1142/S1793042111004101Search in Google Scholar

[18] Parkkonen J. and Paulin F., On the hyperbolic orbital counting problem in conjugacy classes, Math. Z. 279 (2015), no. 3–4, 1175–1196. 10.1007/s00209-015-1408-9Search in Google Scholar

[19] Patterson S. J., A lattice-point problem in hyperbolic space, Mathematika 22 (1975), no. 1, 81–88. 10.1112/S0025579300004526Search in Google Scholar

[20] Phillips R. and Rudnick Z., The circle problem in the hyperbolic plane, J. Funct. Anal. 121 (1994), no. 1, 78–116. 10.1006/jfan.1994.1045Search in Google Scholar

[21] Sarnak P., Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982), no. 2, 229–247. 10.1016/0022-314X(82)90028-2Search in Google Scholar

[22] Selberg A., Equidistribution in discrete groups and the spectral theory of automorphic forms, http://publications.ias.edu/selberg/section/2491. Search in Google Scholar

[23] Tsuzuki M., Spectral square means for period integrals of wave functions on real hyperbolic spaces, J. Number Theory 129 (2009), no. 10, 2387–2438. 10.1016/j.jnt.2009.04.007Search in Google Scholar