Dirichlet series of Rankin-Cohen brackets
Dirichlet series, Modular forms, Quasimodular forms
Journal of Mathematical Analysis and Applications
Given modular forms f and g of weights k and l, respectively, their Rankin-Cohen bracket [f,g]n(k,l) corresponding to a nonnegative integer n is a modular form of weight k+l+2n, and it is given as a linear combination of the products of the form f(r)g(n-r) for 0≤r≤n. We use a correspondence between quasimodular forms and sequences of modular forms to express the Dirichlet series of a product of derivatives of modular forms as a linear combination of the Dirichlet series of Rankin-Cohen brackets. © 2010 Elsevier Inc.
Original Publication Date
DOI of published version
Choie, Young Ju and Lee, Min Ho, "Dirichlet series of Rankin-Cohen brackets" (2011). Faculty Publications. 2024.