|
On Rankin-Cohen brackets for Siegel modular forms
Author(s):
Özlem
Imamoglu;
Olav
K.
Richter
Journal:
Proc. Amer. Math. Soc.
134
(2006),
995-1001.
MSC (2000):
Primary 11F46;
Secondary 11F50, 11F60
Posted:
October 7, 2005
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We determine an explicit formula for a Rankin-Cohen bracket for Siegel modular forms of degree  on a certain subgroup of the symplectic group. Moreover, we lift that bracket via a Poincaré series to a Siegel cusp form on the full symplectic group.
References:
-
- 1.
- Y. Choie, Jacobi forms and the heat operator, Math. Z. 225 (1997), 95-101. MR 1451334 (98c:11042)
- 2.
- -, Jacobi forms and the heat operator II, Illinois J. Math. 42 (1998), no. 2, 179-186. MR 1612731 (99d:11049)
- 3.
- -, Multilinear operators on Siegel modular forms of genus 1 and 2, J. Math. Anal. Appl. 232 (1999), 34-44. MR 1683034 (2000a:11074)
- 4.
- Y. Choie and W. Eholzer, Rankin-Cohen operators for Jacobi and Siegel forms, J. Number Theory 68 (1998), 160-177. MR 1605899 (99b:11050)
- 5.
- Y. Choie and H. Kim, Differential operators on Jacobi forms of several variables, J. Number Theory 82 (2000), 140-163. MR 1755161 (2001g:11069)
- 6.
- H. Cohen, Sums involving the values at negative integers of L-functions and quadratic characters, Math. Ann. 217 (1975), 271-285. MR 0382192 (52:3080)
- 7.
- W. Eholzer and T. Ibukiyama, Rankin-Cohen type differential operators for Siegel modular forms, Internat. J. Math. 9 (1998), no. 4, 443-463. MR 1635181 (2000c:11079)
- 8.
- M. Eichler and D. Zagier, The theory of Jacobi forms, Birkhäuser, Boston, 1985. MR 0781735 (86j:11043)
- 9.
- E. Freitag, Siegelsche Modulfunktionen, Springer, Berlin, Heidelberg, New York, 1983. MR 0871067 (88b:11027)
- 10.
- R. Rankin, The construction of automorphic forms from the derivatives of a given form, J. Indian Math. Soc. 20 (1956), 103-116. MR 0082563 (18:571c)
- 11.
- C. Ziegler, Jacobi forms of higher degree, Abh. Math. Sem. Univ. Hamburg, 59 (1989), 191-224. MR 1049896 (91g:11046)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11F46,
11F50, 11F60
Retrieve articles in all Journals with MSC
(2000):
11F46,
11F50, 11F60
Additional Information:
Özlem
Imamoglu
Affiliation:
Department of Mathematics, Eidgenössische Technische Hochschule, CH-8092, Zürich, Switzerland
Email:
ozlem@math.ethz.ch
Olav
K.
Richter
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203
Email:
richter@unt.edu
DOI:
10.1090/S0002-9939-05-08270-5
PII:
S 0002-9939(05)08270-5
Received by editor(s):
November 8, 2004
Posted:
October 7, 2005
Additional Notes:
The first author was partially supported by the NSF
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2005,
American Mathematical Society
|
Comments: webmaster@ams.org