Abstract:Bringmann, Guerzhoy, Ono, and the author developed an Eichler-Shimura theory for weakly holomorphic modular forms by studying associated period polynomials. Here we include the Eisenstein series in this theory.
- K. Bringmann, P. Guerzhoy, Z. Kent, and K. Ono, Eichler-Shimura theory for mock modular forms, preprint.
- Jan H. Bruinier, Ken Ono, and Robert C. Rhoades, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Math. Ann. 342 (2008), no. 3, 673–693. MR 2430995, DOI 10.1007/s00208-008-0252-1
- P. Guerzhoy, Hecke operators for weakly holomorphic modular forms and supersingular congruences, Proc. Amer. Math. Soc. 136 (2008), no. 9, 3051–3059. MR 2407067, DOI 10.1090/S0002-9939-08-09277-0
- Klaus Haberland, Perioden von Modulformen einer Variabler and Gruppencohomologie. I, II, III, Math. Nachr. 112 (1983), 245–282, 283–295, 297–315 (German). MR 726861, DOI 10.1002/mana.19831120113
- W. Kohnen and D. Zagier, Modular forms with rational periods, Modular forms (Durham, 1983) Ellis Horwood Ser. Math. Appl.: Statist. Oper. Res., Horwood, Chichester, 1984, pp. 197–249. MR 803368
- Y. Manin, Periods of parabolic forms and $p$-adic Hecke series, Math. USSR Sbornik 21 (1973), 371-393.
- Don Zagier, Periods of modular forms and Jacobi theta functions, Invent. Math. 104 (1991), no. 3, 449–465. MR 1106744, DOI 10.1007/BF01245085
- Zachary A. Kent
- Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
- Email: firstname.lastname@example.org
- Received by editor(s): August 17, 2010
- Published electronically: July 12, 2011
- Additional Notes: The author would like to thank Pavel Guerzhoy, Ken Ono, Don Zagier, and the referee for several suggestions that improved this paper.
- Communicated by: Ken Ono
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3789-3794
- MSC (2010): Primary 11F67, 11F03
- DOI: https://doi.org/10.1090/S0002-9939-2011-10770-6
- MathSciNet review: 2823025