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)



Multilinear differential operators on modular forms

Author: Min Ho Lee
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1267-1277
MSC (2000): Primary 11F11, 11F27
Published electronically: December 12, 2003
MathSciNet review: 2053330
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct multilinear differential operators on modular forms and prove that they are essentially unique. We also discuss certain homogeneous polynomials associated to such differential operators as well as some related multilinear differential operators that do not produce modular forms.

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

  • 1. Y. Choie, Multilinear operators on Siegel modular forms of genus $1$ and $2$, J. Math. Anal. Appl. 232 (1999), 34-44. MR 2000a:11074
  • 2. Y. Choie and W. Eholzer, Rankin-Cohen operators for Jacobi and Siegel forms, J. Number Theory 68 (1998), 160-177. MR 99b:11050
  • 3. H. Cohen, Sums involving the values at negative integers of $L$-functions of quadratic characters, Math. Ann. 217 (1975), 271-285. MR 52:3080
  • 4. P. Cohen, Y. Manin, and D. Zagier, Automorphic pseudodifferential operators, Algebraic aspects of nonlinear systems, Birkhäuser, Boston, 1997, pp. 17-47. MR 98e:11054
  • 5. W. Eholzer and T. Ibukiyama, Rankin-Cohen type differential operators for Siegel modular forms, Internat. J. Math. 9 (1998), 443-463. MR 2000c:11079
  • 6. M. H. Lee, Hilbert modular pseudodifferential operators, Proc. Amer. Math. Soc. 129 (2001), 3151-3160. MR 2002k:11068
  • 7. P. Olver, Equivalence, invariants, and symmetry, Cambridge Univ. Press, Cambridge, 1995. MR 96i:58005
  • 8. P. Olver, Classical invariant theory, London Mathematical Society Student Texts, No. 44, Cambridge Univ. Press, Cambridge, 1999. MR 2001g:13009
  • 9. P. Olver and J. Sanders, Transvectants, modular forms, and the Heisenberg algebra, Adv. in Appl. Math. 25 (2000), 252-283. MR 2001j:11016
  • 10. R. Rankin, The construction of automorphic forms from the derivatives of a given form, J. Indian Math. Soc. (N.S.) 20 (1956), 103-116. MR 18:571c
  • 11. B. Schoeneberg, Elliptic modular functions: an introduction, Die Grundlehren der mathematischen Wissenschaften, Band 203, Springer-Verlag, Heidelberg, 1974. MR 54:236
  • 12. A. Unterberger, Quantization and non-holomorphic modular forms, Lecture Notes in Math., vol. 1742, Springer-Verlag, Berlin, 2000. MR 2001k:11079
  • 13. D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57-75. MR 95d:11048

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F11, 11F27

Retrieve articles in all journals with MSC (2000): 11F11, 11F27

Additional Information

Min Ho Lee
Affiliation: Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614

Received by editor(s): January 15, 2003
Published electronically: December 12, 2003
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society