Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Hilbert modular pseudodifferential operators

Author: Min Ho Lee
Journal: Proc. Amer. Math. Soc. 129 (2001), 3151-3160
MSC (2000): Primary 11F41, 35S05
Published electronically: April 9, 2001
MathSciNet review: 1844987
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • 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

Received by editor(s): March 10, 2000
Published electronically: April 9, 2001
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society