2022/10/19 by Kiyokazu Nagatomo, Nagatomo, Kiyokazu, Yuichi Sakai +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2210.10686
openalex publication_date 2022/10/19 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
The aim in this paper is to give expressions for modular linear differential operators of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of canonically defined higher Serre derivatives and an extension of Rankin-Cohen brackets, as well as in terms of quasimodular forms and almost holomorphic modular forms. The last of these descriptions involves the holomorphic projection map. The paper also includes some general results on the theory of quasimodular forms on both cocompact and non-cocompact subgroups of SL2(ℝ), as well as a slight sharpening of a theorem of Martin and Royer on Rankin-Cohen brackets of quasimodular forms