A Restriction Norm Problem for Siegel Modular Forms

Abstract

We establish an asymptotic formula with a power-saving error of the $L^2$-norm of Siegel cusp forms of degree 2 in an average sense when restricted to the imaginary axis. The result is consistent with the Mass Equidistribution Conjecture for Siegel modular forms and the Lindel\"of Hypothesis for some twisted Koecher-Maass series. Along the way, we perform a careful analysis of the Kitaoka formula of degree 2.