A Theta Operator for Siegel Modular Forms (preliminary Version)
نویسنده
چکیده
We define a theta operator between spaces of Siegel modular forms (mod p), generalizing the theta operator for (elliptic) modular forms.
منابع مشابه
Theta Functionswith Harmonic Coe⁄cients over Number Fields
is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg [13] for even n and by Pfetzer [9] for odd n. Shimura [14] generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta s...
متن کاملCrystalline Representations for GL(2) over Quadratic Imaginary Fields
Let K be a quadratic imaginary field and π an irreducible regular algebraic cuspidal automorphic representation of GL(2,AK). Under the assumption that the central character χπ is isomorphic to its complex conjugate, Taylor et al. associated p-adic Galois representations ρπ,p : GK → GL(2,Qp) which are unramified except at finitely many places, and such that the truncated L-function of the Galois...
متن کاملSiegel Eisenstein Series of Arbitrary Level and Theta Series
Introduction. In this paper we consider Siegel modular forms of genus n and arbitrary level q, which do not vanish at all zero dimensional cusps. If such a form is an eigenform of some power T(p)m, m > 1, of the Hecke operator T(p) with respect to at least one prime p = +__1 mod q and if the weight o f f is big enough, r > n + 1, then this form is uniquely determined by the values of f at the z...
متن کاملOn 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 کاملOn the Basis Problem for Siegel-hilbert Modular Forms
In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...
متن کامل