Saito-kurokawa Lifts, L-values for Gl2, and Congruences between Siegel Modular Forms
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چکیده
Saito-Kurokawa Lifts, L-values for GL2, and Congruences Between Siegel ModularForms
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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In this paper we show how one can use an inner product formula of Heim giving the inner product of a pullback Eisenstein series from Sp10 to Sp2×Sp4×Sp4 with a newform on GL2 and a SaitoKurokawa lift to produce congruences between Saito-Kurokawa lifts and non-CAP forms. This congruence is in part controlled by the L-function on GSp4×GL2. The congruence is then used to produce nontrivial torsion...
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There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts.
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In this paper we consider level stripping for genus 2 cuspidal Siegel eigenforms. In particular, we show that it is possible to strip primes from the level of Saito-Kurokawa lifts that arise as theta lifts and weak endoscopic lifts with a mild condition on the associated character. The main ingredients into our results are a level stripping result for elliptic modular forms and the explicit nat...
متن کاملLocal and global Maass relations (expanded version)
We characterize the irreducible, admissible, spherical representations of GSp4(F ) (where F is a p-adic field) that occur in certain CAP representations in terms of relations satisfied by their spherical vector in a special Bessel model. These local relations are analogous to the Maass relations satisfied by the Fourier coefficients of Siegel modular forms of degree 2 in the image of the Saito-...
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تاریخ انتشار 2010