A Restriction Norm Problem for Siegel Modular Forms

TL;DR

This paper proves an asymptotic formula for the restricted $L^2$-norm of degree 2 Siegel cusp forms, supporting conjectures related to their distribution and L-functions, with detailed analysis of the Kitaoka formula.

Contribution

It provides the first asymptotic formula with power-saving error for the restricted $L^2$-norm of Siegel cusp forms of degree 2, linking to key conjectures.

Findings

Asymptotic formula with power-saving error established

Supports the Mass Equidistribution Conjecture for Siegel modular forms

Aligns with the Lindel"of Hypothesis for twisted Koecher-Maass series

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.