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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
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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.

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  • E. Belokolos, A. Bobenko, V. Enol’skii, A. Its, and V. Matveev, Algebro-geometric approach to nonlinear integrable equations, Springer-Verlag, Heidelberg, 1994.
  • Paula Beazley Cohen, Yuri Manin, and Don Zagier, Automorphic pseudodifferential operators, Algebraic aspects of integrable systems, Progr. Nonlinear Differential Equations Appl., vol. 26, Birkhäuser Boston, Boston, MA, 1997, pp. 17–47. MR 1418868
  • L. Dickey, Soliton equations and Hamiltonian systems, World Scientific, Singapore, 1991.
  • Martin Eichler and Don Zagier, The theory of Jacobi forms, Progress in Mathematics, vol. 55, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 781735
  • Eberhard Freitag, Hilbert modular forms, Springer-Verlag, Berlin, 1990. MR 1050763
  • Paul B. Garrett, Holomorphic Hilbert modular forms, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. MR 1008244
  • David Mumford, Tata lectures on theta. II, Progress in Mathematics, vol. 43, Birkhäuser Boston, Inc., Boston, MA, 1984. Jacobian theta functions and differential equations; With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura. MR 742776
  • A. Parshin, On a ring of formal pseudo-differential operators, Proc. Steklov Inst. Math. 224 (1999), 266–280.
  • D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57–75.

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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