|
Sign changes of Hecke eigenvalues of Siegel cusp forms of genus two
Author(s):
Winfried
Kohnen
Journal:
Proc. Amer. Math. Soc.
135
(2007),
997-999.
MSC (2000):
Primary 11F46
Posted:
October 13, 2006
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We shall show that the eigenvalues of a Hecke eigenform of integral weight and genus 2 not contained in the Maass space change signs infinitely often.
References:
-
- 1.
- A. N. Andrianov: Euler products corresponding to Siegel modular forms of genus 2, Russ. Math. Surv. 29, 45-116 (1974) MR 0432552 (55:5540)
- 2.
- S. Böcherer and S. Raghavan: On Fourier coefficients of Siegel modular forms, J. Reine Angew. Math. 384, 80-101 (1988). MR 0929979 (89c:11068)
- 3.
- S. Breulmann: On Hecke eigenforms in the Maass space, Math. Z. 232, no. 3, 527-530 (1999). MR 1719682 (2000j:11066)
- 4.
- M. Eichler and D. Zagier: The theory of Jacobi forms, Progress in Math, vol. 55, Birkhäuser: Boston, 1985. MR 0781735 (86j:11043)
- 5.
- S. A. Evdokimov: A characterization of the Maass space of Siegel cusp forms of genus 2 (in Russian), Mat. Sbornik (154) 112, 133-142 (1980). MR 0575936 (82a:10028)
- 6.
- M. Knopp, W. Kohnen and W. Pribitkin: On the signs of Fourier coefficients of cusp forms, The Ramanujan J. 7, 269-277 (2003). MR 2035806 (2004m:11064)
- 7.
- E. Landau, Über einen Satz von Tschebyschef, Math. Ann. 61, 527-550 (1906).
- 8.
- H. Maass, Siegel's modular forms and Dirichlet series, Lect. Not. in Math. 216, Springer: Berlin, 1971. MR 0344198 (49:8938)
- 9.
- T. Oda: On modular forms associated with indefinite quadratic forms of signature
 , Math. Ann. 231, 97-144 (1977). MR 0466026 (57:5909) - 10.
- R. Weissauer: The Ramanujan conjecture for genus 2 Siegel modular forms (an application of the trace formula). Preprint, Mannheim (1993).
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11F46
Retrieve articles in all Journals with MSC
(2000):
11F46
Additional Information:
Winfried
Kohnen
Affiliation:
Mathematisches Institut, Universität Heidelberg, INF 288, D-69120 Heidelberg, Germany
Email:
winfried@mathi.uni-heidelberg.de
DOI:
10.1090/S0002-9939-06-08570-4
PII:
S 0002-9939(06)08570-4
Received by editor(s):
July 26, 2005
Received by editor(s) in revised form:
November 15, 2005
Posted:
October 13, 2006
Communicated by:
Ken Ono
Copyright of article:
Copyright
2006,
American Mathematical Society
|
Comments: webmaster@ams.org