Local spectral equidistribution for degree two Siegel modular forms in level and weight aspects

Abstract

We prove an equidistribution result for the Satake parameters of the local representations attached to Siegel cusp forms of degree 2 of increasing level and weight, counted with a certain arithmetic weight. We then apply this to compute the symmetry type of a similarly weighted distribution of the low-lying zeros of L-functions attached to these cusp forms.