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arXiv · 1512.07204

Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level

Martin Dickson·Ameya Pitale·Abhishek Saha·Ralf Schmidt
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Abstract

We formulate an explicit refinement of Böcherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve this, we compute the relevant local integrals that appear in the refined global Gan-Gross-Prasad conjecture for Bessel periods as proposed by Yifeng Liu. We note several consequences of our conjecture to arithmetic and analytic properties of L-functions and Fourier coefficients of Siegel modular forms.

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Martin Dickson, Ameya Pitale, Abhishek Saha, Ralf Schmidt. 2019-07-27. Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level. https://arxiv.org/abs/1512.07204

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