On the number of Fourier coefficients that determine a Hilbert modular form
HTML articles powered by AMS MathViewer
- by Srinath Baba, Kalyan Chakraborty and Yiannis N. Petridis PDF
- Proc. Amer. Math. Soc. 130 (2002), 2497-2502 Request permission
Abstract:
We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.References
- Eberhard Freitag, Hilbert modular forms, Springer-Verlag, Berlin, 1990. MR 1050763, DOI 10.1007/978-3-662-02638-0
- Dorian Goldfeld and Jeffrey Hoffstein, On the number of Fourier coefficients that determine a modular form, A tribute to Emil Grosswald: number theory and related analysis, Contemp. Math., vol. 143, Amer. Math. Soc., Providence, RI, 1993, pp. 385–393. MR 1210527, DOI 10.1090/conm/143/01006
- Jonathan Huntley, Spectral multiplicity on products of hyperbolic spaces, Proc. Amer. Math. Soc. 111 (1991), no. 1, 1–12. MR 1031667, DOI 10.1090/S0002-9939-1991-1031667-X
- H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. MR 701565, DOI 10.2307/2374264
- Carlos J. Moreno, Analytic proof of the strong multiplicity one theorem, Amer. J. Math. 107 (1985), no. 1, 163–206. MR 778093, DOI 10.2307/2374461
- M. Ram Murty, Congruences between modular forms, Analytic number theory (Kyoto, 1996) London Math. Soc. Lecture Note Ser., vol. 247, Cambridge Univ. Press, Cambridge, 1997, pp. 309–320. MR 1694998, DOI 10.1017/CBO9780511666179.020
- Walter Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II, Math. Ann. 167 (1966), 292–337; ibid. 168 (1966), 261–324 (German). MR 0243062, DOI 10.1007/BF01361556
- Piatetskii-Shapiro, I. I.: Estimate of the dimensionality of the space of automorphous forms for certain types of discrete groups. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 113 (1957) 980–983.
- Hideo Shimizu, On discontinuous groups operating on the product of the upper half planes, Ann. of Math. (2) 77 (1963), 33–71. MR 145106, DOI 10.2307/1970201
- Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
Additional Information
- Srinath Baba
- Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
- Email: sbaba@math.mcgill.ca
- Kalyan Chakraborty
- Affiliation: School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India
- Email: kalyan@mri.ernet.in
- Yiannis N. Petridis
- Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
- Email: petridis@math.mcgill.ca
- Received by editor(s): February 27, 2001
- Published electronically: April 17, 2002
- Communicated by: Dennis A. Hejhal
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2497-2502
- MSC (2000): Primary 11F41; Secondary 11F30
- DOI: https://doi.org/10.1090/S0002-9939-02-06609-1
- MathSciNet review: 1900854