RANKIN–COHEN TYPE DIFFERENTIAL OPERATORS FOR SIEGEL MODULAR FORMS

DOI10.1142/S0129167X98000191zbMath0919.11037arXivalg-geom/9703033MaRDI QIDQ4217450

Tomoyoshi Ibukiyama, Wolfgang Eholzer

Publication date: 17 August 1999

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9703033

zbMATH Keywords

Siegel modular formsbilinear differential operatorsRankin-Cohen type operatorsspaces of invariant pluriharmonic polynomials

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Hecke-Petersson operators, differential operators (several variables) (11F60)

Related Items

Differential symmetry breaking operators. II: Rankin-Cohen operators for symmetric pairs ⋮ Higher pullbacks of modular forms on orthogonal groups ⋮ Second-order integrable Lagrangians and WDVV equations ⋮ A generating function for Rankin-Cohen brackets ⋮ Differential operators for Siegel-Jacobi forms ⋮ Structure theorems for vector valued Siegel modular forms of degree 2 and weight detk ⊗Sym(10) ⋮ Rankin-Cohen brackets, transvectants and covariant differential operators ⋮ The Lie theory of the Rankin-Cohen brackets and allied bi-differential operators ⋮ Rankin-Cohen brackets on Hilbert modular forms and special values of certain Dirichlet series ⋮ Rankin-Cohen operators for Jacobi and Siegel forms ⋮ Rankin-Cohen brackets and representations of conformal Lie groups ⋮ Rankin-Cohen brackets on Siegel modular forms and special values of certain Dirichlet series ⋮ Construction of modular differential equations by using Rankin-Cohen brackets ⋮ Generalized transvectants and Siegel modular forms ⋮ Derivatives of Siegel modular forms and modular connections ⋮ On mod \(p\) properties of Siegel modular forms ⋮ Differential operators mod \(p\): analytic continuation and consequences ⋮ Differential operators for Hermitian Jacobi forms and Hermitian modular forms ⋮ On vector valued Siegel modular forms of degree 2 with small levels ⋮ Transvectants, modular forms, and the Heisenberg algebra. ⋮ SIMPLE GRADED RINGS OF SIEGEL MODULAR FORMS, DIFFERENTIAL OPERATORS AND BORCHERDS PRODUCTS ⋮ On Rankin-Cohen brackets for Siegel modular forms ⋮ Rankin-Cohen brackets and associativity ⋮ Congruence Primes of the Kim–Ramakrishnan–Shahidi Lift ⋮ Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms ⋮ SYMMETRIC SQUARE L-FUNCTIONS AND SHAFAREVICH–TATE GROUPS, II ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ Vector-valued Siegel modular forms of weight det^k ⊗ Sym(8) ⋮ On p-Adic Properties of Siegel Modular Forms ⋮ On the computation of the determinant of vector-valued Siegel modular forms

Cites Work

• Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• On the Segal-Shale-Weil representations and harmonic polynomials
• On a Class of Linear Differential Equations for Automorphic Forms in Several Complex Variables