Quasimodular forms and Poincaré series

Dirichlet series of Rankin–Cohen brackets

“…The proof of this theorem is carried out by using a correspondence between quasimodular forms and sequences of modular forms discussed in [8]. For example, each quasimodular form can be written as a linear combination derivatives of a finite number of modular forms.…”

“…In this section we describe SL(2, R)-equivariant automorphisms of spaces of polynomials introduced in [8] which determine correspondences between quasimodular polynomials and modular polynomials.…”

Hilbert modular and quasimodular forms

“…These results can be used to show that there is a one-toone correspondence between quasimodular forms (of weight greater than twice the depth) and certain finite sequences of modular forms (cf. [6]). This correspondence may potentially be used to investigate certain properties of quasimodular forms by studying similar properties of the modular forms in the corresponding sequences.…”

Quasimodular Forms and Cohomology

“…for all γ ∈ SL(2, R), where Ξ m λ and Λ m λ are the isomorphisms in (2.6) (see also [5]). We now fix a discrete subgroup Γ of SL(2, R) and consider the restrictions of the SL(2, R) actions described above to Γ.…”

“…It is known that there is a correspondence between quasimodular forms and certain sequences of modular forms (see also [5]). More precisely, a quasimodular form can be expressed as a linear combination of derivatives of the corresponding modular forms.…”