Almost holomorphic modular form

In mathematics, almost holomorphic modular forms are a generalization of modular forms that are polynomials in 1/Im(τ) with coefficients that are holomorphic functions of τ. A quasimodular form is the holomorphic part of an almost holomorphic modular form. The archetypal example of an almost homomorphic modular form is E₂(τ) – 3/πIm(τ), whose holomorphic part is the quasimodular Eisenstein series E₂(τ).

References

• Zagier, Don (2008), "Elliptic modular forms and their applications", The 1-2-3 of modular forms, Universitext, Berlin: Springer, pp. 1–103, doi:10.1007/978-3-540-74119-0, ISBN 978-3-540-74117-6, MR 2409678