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 $\mathbb{H} \times \mathbb{H}$ 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. 
Sheng-Chi Liu and Matthew P. Young
math.NT