5,605 research outputs found
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
in the case that the Siegel form is a
Saito-Kurokawa lift. A formula of Ichino links this behavior to a family of
-functions.Comment: 28 page
Local spectral equidistribution for Siegel modular forms and applications
We study the distribution, in the space of Satake parameters, of local
components of Siegel cusp forms of genus 2 and growing weight, subject to a
specific weighting which allows us to apply results concerning Bessel models
and a variant of Petersson's formula. We obtain for this family a quantitative
local equidistribution result, and derive a number of consequences. In
particular, we show that the computation of the density of low-lying zeros of
the spinor L-functions (for restricted test functions) gives global evidence
for a well-known conjecture of B\"ocherer concerning the arithmetic nature of
Fourier coefficients of Siegel cusp forms.Comment: 45 pages; typos corrected and two references added; version to appear
in Compositio Mat
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