Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts

Matthew P. Young; Sheng-chi Liu

arxiv: 1108.0723 · v1 · pith:UTI2BKFNnew · submitted 2011-08-03 · 🧮 math.NT

Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts

Sheng-chi Liu , Matthew P. Young This is my paper

classification 🧮 math.NT

keywords siegelbehaviorformmathbbmodularsaito-kurokawatimesanalytic

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We study the analytic behavior of the restriction of a Siegel modular form to $\mathbb{H} \times \mathbb{H}$ in the case that the Siegel form is a Saito-Kurokawa lift. A formula of Ichino links this behavior to a family of $GL_3 \times GL_2$ $L$-functions.

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Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts

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