Differential operators on Hermitian modular forms on U(n, n)

2025/06/23 by Takeda, Nobuki
#11F55 #11F60 #11F70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.18236

Abstract

We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We construct explicit bases for the space of such polynomials and use them to build concrete operators. As an application, we derive an exact pullback formula for hermitian Eisenstein series.

Citations

• Pullback formula for vector-valued Hermitian modular forms on U_n,n
• Constructing vector-valued automorphic forms on unitary groups
• Rankin--Cohen Type Differential Operators on Hermitian Modular Forms
• Kurokawa-Mizumoto congruence and differential operators on automorphic forms
• Pullback formula for vector valued Siegel modular forms and its\n applications

Related

• Pullback formula for vector-valued Hermitian modular forms on U_n,n
• Rankin--Cohen Type Differential Operators on Hermitian Modular Forms
• Differential modular forms and some analytic relations between Eisenstein series
• Differential Operators for Siegel-Jacobi forms
• Some aspects of Hermitian Jacobi forms