Dirichlet series of Rankin-Cohen Brackets
YongJu Choie, Min Ho Lee

TL;DR
This paper explores the Dirichlet series associated with Rankin-Cohen brackets of modular forms, expressing them through a correspondence with quasimodular forms and derivatives, revealing new analytical relationships.
Contribution
It introduces a novel method to represent Dirichlet series of derivatives of modular forms using Rankin-Cohen brackets and quasimodular form correspondence.
Findings
Expressed Dirichlet series as linear combinations of Rankin-Cohen brackets
Established a link between quasimodular forms and derivatives of modular forms
Provided new analytical tools for studying modular form products
Abstract
Given modular forms and of weights and , respectively, their Rankin-Cohen bracket corresponding to a nonnegative integer is a modular form of weight , and it is given as a linear combination of the products of the form for . 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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Advanced Combinatorial Mathematics
