Local spectral equidistribution for Siegel modular forms and applications
By Emmanuel Kowalski, Abhishek Saha, Jacob Tsimerman. Compositio Mathematica, 2010
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Abstract We study the distribution, in the space of Satake parameters, of local components of Siegel cusp forms of genus 2 and growing weight k, 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 Böcherer concerning the arithmetic nature of Fourier coefficients of Siegel cusp forms.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ed3d26436cd1efd0d9fc8e0573286a5dfd1e1d33
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In Algebra and Number Theory
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Citations in the corpus
- Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions (2012, background): “See [37,85] for numerical investigations and conjectures and see [40,49,50,53,68,82,84] and the references therein for theoretical results.”