|
Separators of Siegel modular forms of degree two
Author(s):
Bernhard
Heim
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4167-4173.
MSC (2000):
Primary 11Fxx
Posted:
June 26, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that cuspidal Siegel modular forms of degree two and weight are uniquely determined by their Fourier coefficients on small subsets of matrices of content one. This generalizes results of Breulmann, Kohnen, Katsurada, Scharlau and Walling. We give applications to the space of Saito-Kurokawa lifts.
References:
-
- 1.
- A. Atkin, J. Lehner: Hecke operators on
. Math. Ann. 185 (1970), 134-160. MR 0268123 (42:3022) - 2.
- S. Breulmann, W. Kohnen: Twisted Maass-Koecher series and spinor zeta functions. Nagoya Math. J. 155 (1999), 153-160. MR 1711371 (2000g:11033)
- 3.
- W. Casselman: On some results of Atkin and Lehner. Math. Ann. 201 (1973), 301-314. MR 0337789 (49:2558)
- 4.
- B. Heim: On the Spezialschar of Maass. arXiv: 0801.1804v1 [math.NT].
- 5.
- H. Katsurada: On the coincidence of Hecke-eigenforms. Abh. Math. Sem. Univ. Hamburg, 70 (2000), 77-83. MR 1809535 (2001k:11083)
- 6.
- K. Ono, C. Skinner: Fourier coefficients of half-integral weight modular forms modulo
. Annals of Math. (2) 147 (1998), 453-470. MR 1626761 (99f:11059a) - 7.
- C. Poor, D. Yuen: Linear dependence among Siegel modular forms. Math. Ann. 318 (2000), 205-234. MR 1795560 (2001j:11024)
- 8.
- C.S. Rajan: Refinement of strong multiplicity one for automorphic representations of Gl
. Proc. Amer. Math. Soc. 128 (2000), 691-700. MR 1707005 (2000g:11041) - 9.
- C.S. Rajan: On strong multiplicity one for
-adic representations. IMRN 3 (1998), 161-172. MR 1606395 (99c:11064) - 10.
- D. Ramakrishnan: A refinement of the strong multiplicity one theorem for GL
. Invent. Math. 116 (1994), 645-649. MR 1253208 (95h:11050b) - 11.
- R. Scharlau, L. Walling: A weak multiplicity-one theorem for Siegel modular forms. Pacific J. Math. 211 (2003), 369-374. MR 2015741 (2004k:11069)
- 12.
- G. Shimura: Introduction to the Arithmetic Theory of Automorphic Functions. Iwanami Shoten, Tokyo, and Princeton Univ. Press, 1971. MR 0314766 (47:3318)
- 13.
- D. Zagier: Sur la conjecture de Saito-Kurokawa (d'après H. Maass). Sém. Delange-Pisot-Poitou 1979/1980, Progress in Math. 12, Birkhäuser, Boston, 1981, 371-394. MR 633910 (83b:10031)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11Fxx
Retrieve articles in all Journals with MSC
(2000):
11Fxx
Additional Information:
Bernhard
Heim
Affiliation:
Max-Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Email:
heim@mpim-bonn.mpg.de
DOI:
10.1090/S0002-9939-08-09597-X
PII:
S 0002-9939(08)09597-X
Received by editor(s):
November 8, 2007
Posted:
June 26, 2008
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2008,
Bernhard Heim
|