On the Transcendence Degree of the Differential Field Generated by Siegel Modular Forms
نویسنده
چکیده
and Hg is open in Zg(C); τ = (τjl) a generic point on Hg, so that k(2πiτ ) can be viewed as the field of rational functions on Zg/k; Γ = a congruence subgroup of Sp2g(Z) (equivalently, a subgroup of finite index if g > 1). We recall that the symplectic group Sp2g has dimension dimSp2g = 2g 2 + g; Rw(Γ, k) = k-vector-space of k-rational modular forms of weight w (a non-negative integer) relative to Γ, i.e. holomorphic functions f on Hg which satisfy
منابع مشابه
On Atkin-Lehner correspondences on Siegel spaces
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime l...
متن کاملHecke Operators 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 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 کاملMultilinear Operators on Siegel Modular Forms of Genus
Classically, there are many interesting connections between differential operators and the theory of elliptic modular forms and many interesting results have been explored. In particular, it has been known for some time how to obtain an elliptic modular form from the derivatives ofN elliptic modular forms, which has already been studied in detail by R. Rankin in [9] and [10]. When N = 2, as a s...
متن کاملRamanujan Congruences for Siegel Modular Forms
We determine conditions for the existence and non-existence of Ramanujan-type congruences for Jacobi forms. We extend these results to Siegel modular forms of degree 2 and as an application, we establish Ramanujan-type congruences for explicit examples of Siegel modular forms.
متن کامل