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We study the distribution, in the space of Satake parameters, of localcomponents of Siegel cusp forms of genus 2 and growing weight, subject to aspecific weighting which allows us to apply results concerning Bessel modelsand a variant of Petersson's formula. We obtain for this family a quantitativelocal equidistribution result, and derive a number of consequences. Inparticular, we show that the computation of the density of low-lying zeros ofthe spinor L-functions (for restricted test functions) gives global evidencefor a well-known conjecture of B\"ocherer concerning the arithmetic nature ofFourier coefficients of Siegel cusp forms.

Local spectral equidistribution for Siegel modular forms and applications