Quasimodular forms and quasimodular polynomials
[Formes quasimodulaires et polynômes quasimodulaires]
Annales mathématiques Blaise Pascal, Tome 19 (2012) no. 2, pp. 431-453.

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.

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.

DOI : 10.5802/ambp.318

Min Ho Lee 1

1 Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 U.S.A
@article{AMBP_2012__19_2_431_0,
     author = {Min Ho Lee},
     title = {Quasimodular forms and quasimodular polynomials},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {431--453},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {19},
     number = {2},
     year = {2012},
     doi = {10.5802/ambp.318},
     mrnumber = {3025140},
     zbl = {1283.11071},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.318/}
}
TY  - JOUR
AU  - Min Ho Lee
TI  - Quasimodular forms and quasimodular polynomials
JO  - Annales mathématiques Blaise Pascal
PY  - 2012
SP  - 431
EP  - 453
VL  - 19
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.318/
DO  - 10.5802/ambp.318
LA  - en
ID  - AMBP_2012__19_2_431_0
ER  - 
%0 Journal Article
%A Min Ho Lee
%T Quasimodular forms and quasimodular polynomials
%J Annales mathématiques Blaise Pascal
%D 2012
%P 431-453
%V 19
%N 2
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.318/
%R 10.5802/ambp.318
%G en
%F AMBP_2012__19_2_431_0
Min Ho Lee. Quasimodular forms and quasimodular polynomials. Annales mathématiques Blaise Pascal, Tome 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

Cité par Sources :