Quasimodular forms and quasimodular polynomials
Annales mathématiques Blaise Pascal, Volume 19 (2012) no. 2, pp. 431-453.

This paper is based on lectures delivered at the Workshop on quasimodular forms held in June, 2010 in Besse, France, and it provides a survey of some recent work on quasimodular forms.

Ce texte a pour origine des cours donnés à l’École d’été sur les formes quasimodulaires qui s’est tenue en juin 2010 à Besse, France. Il contient une présentation de travaux récents sur les formes quasimodulaires.

DOI: 10.5802/ambp.318
Min Ho Lee 1

1 Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 U.S.A
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Min Ho Lee. Quasimodular forms and quasimodular polynomials. Annales mathématiques Blaise Pascal, Volume 19 (2012) no. 2, pp. 431-453. doi : 10.5802/ambp.318. https://ambp.centre-mersenne.org/articles/10.5802/ambp.318/

[1] Y. Choie; M. H. Lee Quasimodular forms, Jacobi-like forms, and pseudodifferential operators (preprint)

[2] Paula Beazley Cohen; Yuri Manin; Don Zagier Automorphic pseudodifferential operators, Algebraic aspects of integrable systems (Progr. Nonlinear Differential Equations Appl.), Volume 26, Birkhäuser Boston, Boston, MA, 1997, pp. 17-47 | MR | Zbl

[3] Martin Eichler; Don Zagier The theory of Jacobi forms, Progress in Mathematics, 55, Birkhäuser Boston Inc., Boston, MA, 1985 | MR | Zbl

[4] Alex Eskin; Andrei Okounkov Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math., Volume 145 (2001) no. 1, pp. 59-103 | DOI | MR | Zbl

[5] Masanobu Kaneko; Don Zagier A generalized Jacobi theta function and quasimodular forms, The moduli space of curves (Texel Island, 1994) (Progr. Math.), Volume 129, Birkhäuser Boston, Boston, MA, 1995, pp. 165-172 | MR | Zbl

[6] Min Ho Lee Quasimodular forms and Poincaré series, Acta Arith., Volume 137 (2009) no. 2, pp. 155-169 | DOI | MR | Zbl

[7] Min Ho Lee Quasimodular forms and vector bundles, Bull. Aust. Math. Soc., Volume 80 (2009) no. 3, pp. 402-412 | DOI | MR | Zbl

[8] Min Ho Lee Radial heat operators on Jacobi-like forms, Math. J. Okayama Univ., Volume 51 (2009), pp. 27-46 | MR

[9] Min Ho Lee Heat operators and quasimodular forms, Bull. Aust. Math. Soc., Volume 81 (2010) no. 3, pp. 514-522 | DOI | MR | Zbl

[10] Min Ho Lee Modular polynomials and derivatives of quasimodular forms (2012) (To appear in Complex Variables and Elliptic Equations) | DOI

[11] Min Ho Lee Quasimodular forms and cohomology, Bull. Aust. Math. Soc., Volume 86 (2012), pp. 150-163 | DOI

[12] Samuel Lelièvre; Emmanuel Royer Orbitwise countings in (2) and quasimodular forms, Int. Math. Res. Not. (2006), pp. Art. ID 42151, 30 | DOI | MR | Zbl

[13] François Martin; Emmanuel Royer Formes modulaires et périodes, Formes modulaires et transcendance (Sémin. Congr.), Volume 12, Soc. Math. France, Paris, 2005, pp. 1-117 | MR | Zbl

[14] Toshitsune Miyake Modular forms, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2006 (Translated from the 1976 Japanese original by Yoshitaka Maeda) | MR | Zbl

[15] Hossein Movasati On differential modular forms and some analytic relations between Eisenstein series, Ramanujan J., Volume 17 (2008) no. 1, pp. 53-76 | DOI | MR | Zbl

[16] A. Okounkov; R. Pandharipande Gromov-Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. (2), Volume 163 (2006) no. 2, pp. 517-560 | DOI | MR | Zbl

[17] Najib Ouled Azaiez The ring of quasimodular forms for a cocompact group, J. Number Theory, Volume 128 (2008) no. 7, pp. 1966-1988 | DOI | MR | Zbl

[18] Y. H. Rhie; G. Whaples Hecke operators in cohomology of groups, J. Math. Soc. Japan, Volume 22 (1970), pp. 431-442 | DOI | MR | Zbl

[19] Emmanuel Royer Evaluating convolution sums of the divisor function by quasimodular forms, Int. J. Number Theory, Volume 3 (2007) no. 2, pp. 231-261 | DOI | MR | Zbl

[20] Don Zagier Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci., Volume 104 (1994) no. 1, pp. 57-75 (K. G. Ramanathan memorial issue) | DOI | MR | Zbl

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