Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts
نویسندگان
چکیده
منابع مشابه
Growth and Nonvanishing of Restricted Siegel Modular Forms Arising as Saito-kurokawa Lifts
We study the analytic behavior of the restriction of a Siegel modular form to H × H in the case that the Siegel form is a Saito-Kurokawa lift. A formula of Ichino links this behavior to a family of GL3 ×GL2 L-functions.
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Saito-Kurokawa Lifts, L-values for GL2, and Congruences Between Siegel ModularForms
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Let f ∈ S2κ−2(Γ0(M)) be a Hecke eigenform with κ ≥ 2 even and M ≥ 1 and odd and square-free. In this paper we survey the construction of the Saito-Kurokawa lifting from the classical and representation theoretic point of view. We also provide some arithmetic results on the Fourier coefficients of Saito-Kurokawa liftings. We then calculate the norm of the Saito-Kurokawa lift.
متن کاملSaito-kurokawa Lifts and Applications to Arithmetic
In this short survey paper we present an outline for using the Saito-Kurokawa correspondence to provide evidence for the Bloch-Kato conjecture for modular forms. Specific results will be stated, but the aim is to provide the framework for such results with an aim towards future research. 1. The Bloch-Kato conjecture for modular forms In this section we will review the Bloch-Kato conjecture for ...
متن کاملSaito-Kurokawa Lifts and Applications to the Bloch-Kato Conjecture
Let f be a newform of weight 2k−2 and level 1. In this paper we provide evidence for the Bloch-Kato conjecture for modular forms. We demonstrate an implication that under suitable hypotheses if ̟ | Lalg(k, f) then p | #Hf (Q,Wf (1− k)) where p is a suitably chosen prime and ̟ a uniformizer of a finite extension K/Qp. We demonstrate this by establishing a congruence between the Saito-Kurokawa lift...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2014
ISSN: 1080-6377
DOI: 10.1353/ajm.2014.0008