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On the number of Fourier coefficients that determine a Hilbert modular form
Author(s):
Srinath
Baba;
Kalyan
Chakraborty;
Yiannis
N.
Petridis
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2497-2502.
MSC (2000):
Primary 11F41;
Secondary 11F30
Posted:
April 17, 2002
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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:
- 1.
- Freitag, E.: Hilbert Modular Forms. Springer Verlag, New York, Berlin, Heidelberg, 1990. MR 91c:11025
- 2.
- Goldfeld, D.; Hoffstein, J.: On the number of Fourier coefficients that determine a modular form. A tribute to Emil Grosswald: number theory and related analysis, 385-393, Contemp. Math., 143, Amer. Math. Soc., Providence, RI, 1993. MR 94b:11037
- 3.
- Huntley, J.: Spectral multiplicity on products of hyperbolic spaces. Proc. Amer. Math. Soc. 111 (1991), no. 1, 1-12. MR 91d:11055
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- Murty, M. R.: Congruences between modular forms. Analytic number theory (Kyoto, 1996), 309-320, London Math. Soc. Lecture Note Ser., 247, Cambridge Univ. Press, Cambridge, 1997. MR 2000c:11073
- 7.
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- 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.
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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
DOI:
10.1090/S0002-9939-02-06609-1
PII:
S 0002-9939(02)06609-1
Keywords:
Hilbert modular forms,
Fourier coefficients
Received by editor(s):
February 27, 2001
Posted:
April 17, 2002
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2002,
American Mathematical Society
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