Differential operators for Siegel-Jacobi forms
نویسندگان
چکیده
منابع مشابه
Rankin-Cohen Operators for Jacobi and Siegel Forms
For any non-negative integer v we construct explicitly ⌊v2⌋+1 independent covariant bilinear differential operators from Jk,m × Jk′,m′ to Jk+k′+v,m+m′ . As an application we construct a covariant bilinear differential operator mapping S (2) k ×S (2) k′ to S (2) k+k′+v. Here Jk,m denotes the space of Jacobi forms of weight k and index m and S (2) k the space of Siegel modular forms of degree 2 a...
متن کاملA Note on Invariant Differential Operators on Siegel-jacobi Space
For two positive integers m and n, we let Hn be the Siegel upper half plane of degree n and let C be the set of all m × n complex matrices. In this article, we investigate differential operators on the Siegel-Jacobi space Hn ×C(m,n) that are invariant under the natural action of the Jacobi group Sp(n,R)⋉ H (n,m) R on Hn × C, where H R denotes the Heisenberg group.
متن کاملEstimating Siegel Modular Forms of Genus 2 Using Jacobi Forms
We give a new elementary proof of Igusa's theorem on the structure of Siegel modular forms of genus 2. The key point of the proof is the estimation of the dimension of Jacobi forms appearing in the FourierJacobi development of Siegel modular forms. This proves not only Igusa's theorem, but also gives the canonical lifting from Jacobi forms to Siegel modular forms of genus 2.
متن کاملDifferential Operators on Jacobi Forms of Several Variables
The theory of the classical Jacobi forms on H × C has been studied extensively by Eichler and Zagier[?]. Ziegler[?] developed a more general approach of Jacobi forms of higher degree. In [?] and [?], Gritsenko and Krieg studied Jacobi forms on H × Cn and showed that these kinds of Jacobi forms naturally arise in the Jacobi Fourier expansions of all kinds of automorphic forms in several variable...
متن کاملOperators on Hilbert - Siegel Modular Forms
We define Hilbert-Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert-Siegel forms (i.e. with arbitrary Siegel d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Science China Mathematics
سال: 2015
ISSN: 1674-7283,1869-1862
DOI: 10.1007/s11425-015-5111-4