Quasimodular forms and quasimodular polynomials
type: Item
instance of: scholarly article
title: Quasimodular forms and quasimodular polynomials
zbMATH Open document ID: 1283.11071
author: Min Ho Lee
published in: Annales Mathématiques Blaise Pascal
publication date: 2013-01-24T00:00:00Z
review text: In this nice expository article, the author provides some recent developments in the theory of quasi-modular forms. Let \(\Gamma\) be a discrete subgroup of \(SL_2(\mathbb R)\). First, the author describes the relations between quasi modular forms, quasi modular polynomials and modular polynomials for \(\Gamma\). Then the author identifies quasi-modular forms for \(\Gamma\) as sections of some vector bundles over the quotient space \(\Gamma \setminus \mathcal{H}\). This generalises the notion of modular forms for \(\Gamma\) as holomorphic sections of line bundles over \(\Gamma \setminus \mathcal{H}\). Next the author discusses the connections of quasi-modular polynomials with Jacobi-like forms. Finally, the author describes a Hecke equivariant linear map from quasi modular forms for \(\Gamma\) to cohomology classes of \(\Gamma\).
reviewed by: Sanoli Gun
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F23
zbMATH DE Number: 6128507
MaRDI profile type: Publication
full work available at URL: ambp.318
OpenAlex ID: W2316363049
cites work: Quasimodular forms and Jacobi-like forms
cites work: Q4718264
cites work: The theory of Jacobi forms
cites work: Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
cites work: Q4858409
cites work: Quasimodular forms and Poincaré series
cites work: QUASIMODULAR FORMS AND VECTOR BUNDLES
cites work: Q3606382
cites work: HEAT OPERATORS AND QUASIMODULAR FORMS
cites work: Modular polynomials and derivatives of quasimodular forms
cites work: Quasimodular forms and cohomology
cites work: Orbitwise countings in H(2) and quasimodular forms
cites work: Q5482664
cites work: Modular Forms
cites work: On differential modular forms and some analytic relations between Eisenstein series
cites work: Gromov-Witten theory, Hurwitz theory, and completed cycles
cites work: The ring of quasimodular forms for a cocompact group
cites work: Hecke operators in cohomology of groups
cites work: EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS
cites work: Modular forms and differential operators
DOI: 10.5802/AMBP.318
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description: scientific article; zbMATH DE number 6128507