Differential algebras of quasi-Jacobi forms of index zero

2024/10/15 by Dumas, François, Martin, François, Royer, Emmanuel
#FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2410.11344

Abstract

The notion of double depth associated with quasi-Jacobi forms allows distinguishing, within the algebra of quasi-Jacobi singular forms of index zero, certain significant subalgebras (modular-type forms, elliptic-type forms, Jacobi forms). We study the stability of these subalgebras under the derivations of this algebra and through certain sequences of bidifferential operators constituting analogs of Rankin-Cohen brackets or transvectants

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