On the cuspidality of pullbacks of Siegel Eisenstein series to Sp2m×Sp2n
نویسنده
چکیده
In this paper we study the pullback of a Siegel Eisenstein series on Sp2m+2n to Sp2m×Sp2n. There is a well-established literature on such pullbacks. In the case that m = n Garrett showed that the pullback is actually a cusp form in each variable separately. Here we generalize this result showing the pullback is cuspidal in the smaller variable in the case m 6= n. Such results have applications to producing congruences between Siegel modular forms.
منابع مشابه
On the Cuspidality of Pullbacks of Siegel Eisenstein Series and Applications to the Bloch–Kato Conjecture
Let k > 9 be an even integer and p a prime with p > 2k− 2. Let f be a newform of weight 2k− 2 and level SL2(Z) so that f is ordinary at p and ρ f,p is irreducible. Under some additional hypotheses, we prove that ordp(Lalg(k, f)) ≤ ordp(#S), where S is the Pontryagin dual of the Selmer group associated to ρ f,p ⊗ ε1−k with ε the p-adic cyclotomic character. We accomplish this by first constructi...
متن کامل2 5 Ju n 20 09 On the Siegel - Weil Theorem for Loop Groups ( II ) Howard Garland
This is the second of our two papers on the Siegel-Weil theorem for loop groups. In the first paper [3] we proved the Siegel-Weil theorem for (finite dimensional) snt-modules ([3], Theorem 8.1). In the present paper we use this result to obtain the Siegel-Weil theorem for loop groups, Theorem 7.5, below. In addition to the corresponding result for snt-modules, our proof depends on a convergence...
متن کاملPULLBACKS OF EISENSTEIN SERIES FROM GU(3, 3) AND CRITICAL L-VALUES FOR GSp(4)×GL(2)
Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight l. We prove a pullback formula for certain Eisenstein series — thus generalizing a construction of Shimura — and use this to derive an explicit integral representation for the degree eight L-function L(s, F × g). This integral representation involves the pullback of a simple Siegel-type ...
متن کاملPullbacks of Eisenstein Series on U(3, 3) and Non-vanishing of Shafarevich-tate Groups
In this paper we construct a pullback formula of a Siegel Eisenstein series on GU(3, 3) to GSp(4) × GL(2) and use it to study the Bloch-Kato conjecture for automorphic forms on GL(2). Let f ∈ S2k−2(SL2(Z)) be a normalized eigenform and let p > 2k− 2 be a prime so that p | Lalg(k, f). Then up to some reasonable hypotheses, we use this formula to construct a congruence between the Saito-Kurokawa ...
متن کاملA p-adic family of Klingen - Eisenstein series
The p-adic interpolation properties of Fourier coefficients of elliptic Eisenstein series are by now classical. These properties can be considered as the starting point and as an important tool in the theory of p-adic L-functions and p-adic families of modular forms. In the case of Siegel modular forms there are two types of Eisenstein series. A Siegel Eisenstein measure which comes from the Si...
متن کامل