2025/02/14 by Hicham Saber, Saber, Hicham, Abdellah Sebbar +1
Mathematics · #Algebraic structures and combinatorial models #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2502.10176
openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to quasimodular forms and equivariant functions. We prove that a meromorphic function is equivariant if and only if its higher Schwarzians are quasimodular forms of prescribed weight and depth, thereby extending classical results and linking projective differential operators to the structure of modular and quasimodular forms.