Quasimodular forms and quasimodular polynomials

Min Ho Lee[1]

  • [1] Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 U.S.A

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 2, page 431-453
  • ISSN: 1259-1734

Abstract

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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.

How to cite

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Lee, Min Ho. "Quasimodular forms and quasimodular polynomials." Annales mathématiques Blaise Pascal 19.2 (2012): 431-453. <http://eudml.org/doc/251077>.

@article{Lee2012,
abstract = {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.},
affiliation = {Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 U.S.A},
author = {Lee, Min Ho},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {7},
number = {2},
pages = {431-453},
publisher = {Annales mathématiques Blaise Pascal},
title = {Quasimodular forms and quasimodular polynomials},
url = {http://eudml.org/doc/251077},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Lee, Min Ho
TI - Quasimodular forms and quasimodular polynomials
JO - Annales mathématiques Blaise Pascal
DA - 2012/7//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 2
SP - 431
EP - 453
AB - 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.
LA - eng
UR - http://eudml.org/doc/251077
ER -

References

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  1. Y. Choie, M. H. Lee, Quasimodular forms, Jacobi-like forms, and pseudodifferential operators Zbl1327.11027
  2. Paula Beazley Cohen, Yuri Manin, Don Zagier, Automorphic pseudodifferential operators, Algebraic aspects of integrable systems 26 (1997), 17-47, Birkhäuser Boston, Boston, MA Zbl1055.11514MR1418868
  3. Martin Eichler, Don Zagier, The theory of Jacobi forms, 55 (1985), Birkhäuser Boston Inc., Boston, MA Zbl0554.10018MR781735
  4. Alex Eskin, Andrei Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001), 59-103 Zbl1019.32014MR1839286
  5. Masanobu Kaneko, Don Zagier, A generalized Jacobi theta function and quasimodular forms, The moduli space of curves (Texel Island, 1994) 129 (1995), 165-172, Birkhäuser Boston, Boston, MA Zbl0892.11015MR1363056
  6. Min Ho Lee, Quasimodular forms and Poincaré series, Acta Arith. 137 (2009), 155-169 Zbl1207.11050MR2491534
  7. Min Ho Lee, Quasimodular forms and vector bundles, Bull. Aust. Math. Soc. 80 (2009), 402-412 Zbl1225.11051MR2569915
  8. Min Ho Lee, Radial heat operators on Jacobi-like forms, Math. J. Okayama Univ. 51 (2009), 27-46 Zbl1257.11047MR2482404
  9. Min Ho Lee, Heat operators and quasimodular forms, Bull. Aust. Math. Soc. 81 (2010), 514-522 Zbl1213.11096MR2639868
  10. Min Ho Lee, Modular polynomials and derivatives of quasimodular forms, (2012) Zbl1304.11023
  11. Min Ho Lee, Quasimodular forms and cohomology, Bull. Aust. Math. Soc. 86 (2012), 150-163 Zbl1277.11032
  12. Samuel Lelièvre, Emmanuel Royer, Orbitwise countings in ℋ ( 2 ) and quasimodular forms, Int. Math. Res. Not. (2006) Zbl1142.11025MR2233718
  13. François Martin, Emmanuel Royer, Formes modulaires et périodes, Formes modulaires et transcendance 12 (2005), 1-117, Soc. Math. France, Paris Zbl1104.11017MR2186573
  14. Toshitsune Miyake, Modular forms, (2006), Springer-Verlag, Berlin Zbl1159.11014MR2194815
  15. Hossein Movasati, On differential modular forms and some analytic relations between Eisenstein series, Ramanujan J. 17 (2008), 53-76 Zbl1244.11041MR2439525
  16. A. Okounkov, R. Pandharipande, Gromov-Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. (2) 163 (2006), 517-560 Zbl1105.14076MR2199225
  17. Najib Ouled Azaiez, The ring of quasimodular forms for a cocompact group, J. Number Theory 128 (2008), 1966-1988 Zbl1198.11042MR2423744
  18. Y. H. Rhie, G. Whaples, Hecke operators in cohomology of groups, J. Math. Soc. Japan 22 (1970), 431-442 Zbl0211.34705MR285620
  19. Emmanuel Royer, Evaluating convolution sums of the divisor function by quasimodular forms, Int. J. Number Theory 3 (2007), 231-261 Zbl1142.11027MR2333619
  20. Don Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57-75 Zbl0806.11022MR1280058

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