Faculty Publications

Dirichlet Series Of Rankin-Cohen Brackets

Document Type

Article

Keywords

Dirichlet series, Modular forms, Quasimodular forms

Journal/Book/Conference Title

Journal of Mathematical Analysis and Applications

Volume

373

Issue

2

First Page

464

Last Page

474

Abstract

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.

Department

Department of Mathematics

Original Publication Date

1-1-2011

DOI of published version

10.1016/j.jmaa.2010.07.055

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