|
Hilbert modular pseudodifferential operators
Author(s):
Min
Ho
Lee
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3151-3160.
MSC (2000):
Primary 11F41, 35S05
Posted:
April 9, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We introduce Jacobi-like forms of several variables, and study their connections with Hilbert modular forms and pseudodifferential operators of several variables. We also construct Rankin-Cohen brackets for Hilbert modular forms using such Jacobi-like forms.
References:
-
- 1.
- E. Belokolos, A. Bobenko, V. Enol'skii, A. Its, and V. Matveev, Algebro-geometric approach to nonlinear integrable equations, Springer-Verlag, Heidelberg, 1994.
- 2.
- P. Cohen, Y. Manin, and D. Zagier, Automorphic pseudodifferential operators, Algebraic aspects of nonlinear systems, Birkhäuser, Boston, 1997, pp. 17-47. MR 98e:11054
- 3.
- L. Dickey, Soliton equations and Hamiltonian systems, World Scientific, Singapore, 1991.
- 4.
- M. Eichler and D. Zagier, The theory of Jacobi forms, Progress in Math., vol. 55, Birkhäuser, Boston, 1985. MR 86j:11043
- 5.
- E. Freitag, Hilbert modular forms, Springer-Verlag, Heidelberg, 1990. MR 91c:11025
- 6.
- P. Garrett, Holomorphic Hilbert modular forms, Wadsworth, Belmont, 1990. MR 90k:11058
- 7.
- D. Mumford, Tata lectures on theta II, Birkhäuser, Boston, 1984. MR 86b:14017
- 8.
- A. Parshin, On a ring of formal pseudo-differential operators, Proc. Steklov Inst. Math. 224 (1999), 266-280.
- 9.
- D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57-75.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11F41, 35S05
Retrieve articles in all Journals with MSC
(2000):
11F41, 35S05
Additional Information:
Min
Ho
Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614
Email:
lee@math.uni.edu
DOI:
10.1090/S0002-9939-01-06117-2
PII:
S 0002-9939(01)06117-2
Received by editor(s):
March 10, 2000
Posted:
April 9, 2001
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org